My solution was :

• put dummy empty divs in between with a max-height specified
• change space-between to flex-start
• set the content blocks to nogrow
• set the dummy divs to grow

Then the spaces grow up to a max specified.

Key differences between justify-content, justify-items and justify-self in CSS Grid:

• The justify-content property controls the alignment of grid columns. It is set on the grid container. It does not apply to or control the alignment of grid items.
• The justify-items property controls the alignment of grid items. It is set on the grid container.
• The justify-self property overrides justify-items on individual items. It is set on grid items and inherits the value of justify-items, by default.

Example

Here's a 2x3 grid.

• 2 columns, each 100px wide
• 3 rows, each 50px tall

The container is:

• 500px wide
• 250px tall

.container {
    display: grid;
    grid-template-columns: 100px 100px;
    grid-template-rows: 50px 50px 50px;
    width: 500px;
    height: 250px;
    grid-template-areas: " one two"
                         " three four"
                         " five six ";
}

.box:nth-child(1) {  grid-area: one;   }
.box:nth-child(2) {  grid-area: two;   }
.box:nth-child(3) {  grid-area: three; }
.box:nth-child(4) {  grid-area: four;  }
.box:nth-child(5) {  grid-area: five;  }
.box:nth-child(6) {  grid-area: six;   }

/* non-essential decorative styles */
body {
    display: flex;
    justify-content: center;
}
.container {
    background-color: #ddd;
    border: 1px solid #aaa;
}
.box {
    background-color: lightgreen;
    border: 1px solid gray;
    display: flex;
    justify-content: center;
    align-items: center;
    font-size: 1.2em;
}

<div class="container">
    <div class="box"><span>1</span></div>
    <div class="box"><span>2</span></div>
    <div class="box"><span>3</span></div>
    <div class="box"><span>4</span></div>
    <div class="box"><span>5</span></div>
    <div class="box"><span>6</span></div>    
</div>

justify-content

The justify-content property aligns columns within the container.

.container {
  justify-content: space-between;
}

.container {
    display: grid;
    grid-template-columns: 100px 100px;
    grid-template-rows: 50px 50px 50px;
    width: 500px;
    height: 250px;
    grid-template-areas: " one two"
                         " three four"
                         " five six ";
}

.box:nth-child(1) {  grid-area: one;   }
.box:nth-child(2) {  grid-area: two;   }
.box:nth-child(3) {  grid-area: three; }
.box:nth-child(4) {  grid-area: four;  }
.box:nth-child(5) {  grid-area: five;  }
.box:nth-child(6) {  grid-area: six;   }

/* non-essential decorative styles */
body {
    display: flex;
    justify-content: center;
}
.container {
    background-color: #ddd;
    border: 1px solid #aaa;
}
.box {
    background-color: lightgreen;
    border: 1px solid gray;
    display: flex;
    justify-content: center;
    align-items: center;
    font-size: 1.2em;
}

<div class="container">
    <div class="box"><span>1</span></div>
    <div class="box"><span>2</span></div>
    <div class="box"><span>3</span></div>
    <div class="box"><span>4</span></div>
    <div class="box"><span>5</span></div>
    <div class="box"><span>6</span></div>    
</div>

With justify-content: space-between both columns are pinned to the edges. The grid items shift only because they exist inside those columns. They are otherwise unaffected.

Note that this property works only when there is free space in the container. If any of the columns were sized with fr, then all free space would be consumed, and justify-content would have no effect.

justify-items

The justify-items property aligns grid items within their tracks (not the entire container)

.container {
  justify-items: center;
}

.container {
    display: grid;
    grid-template-columns: 100px 100px;
    grid-template-rows: 50px 50px 50px;
    width: 500px;
    height: 250px;
    grid-template-areas: " one two"
                         " three four"
                         " five six ";
}

.box:nth-child(1) {  grid-area: one;   }
.box:nth-child(2) {  grid-area: two;   }
.box:nth-child(3) {  grid-area: three; }
.box:nth-child(4) {  grid-area: four;  }
.box:nth-child(5) {  grid-area: five;  }
.box:nth-child(6) {  grid-area: six;   }

/* non-essential decorative styles */
body {
    display: flex;
    justify-content: center;
}
.container {
    background-color: #ddd;
    border: 1px solid #aaa;
}
.box {
    background-color: lightgreen;
    border: 1px solid gray;
    display: flex;
    justify-content: center;
    align-items: center;
    font-size: 1.2em;
}

<div class="container">
    <div class="box"><span>1</span></div>
    <div class="box"><span>2</span></div>
    <div class="box"><span>3</span></div>
    <div class="box"><span>4</span></div>
    <div class="box"><span>5</span></div>
    <div class="box"><span>6</span></div>    
</div>

With justify-items: center the grid items are centered within their columns.

justify-self

The justify-self property overrides justify-items on individual items.

.container        { justify-items: center;}
.box:nth-child(2) { justify-self: start; }
.box:nth-child(3) { justify-self: end; }
.box:nth-child(6) { justify-self: stretch; }


.container {
    display: grid;
    grid-template-columns: 100px 100px;
    grid-template-rows: 50px 50px 50px;
    width: 500px;
    height: 250px;
    grid-template-areas: " one two"
                         " three four"
                         " five six ";
}

.box:nth-child(1) {  grid-area: one;   }
.box:nth-child(2) {  grid-area: two;   }
.box:nth-child(3) {  grid-area: three; }
.box:nth-child(4) {  grid-area: four;  }
.box:nth-child(5) {  grid-area: five;  }
.box:nth-child(6) {  grid-area: six;   }

/* non-essential decorative styles */
body {
    display: flex;
    justify-content: center;
}
.container {
    background-color: #ddd;
    border: 1px solid #aaa;
}
.box {
    background-color: lightgreen;
    border: 1px solid gray;
    display: flex;
    justify-content: center;
    align-items: center;
    font-size: 1.2em;
}

<div class="container">
    <div class="box"><span>1</span></div>
    <div class="box"><span>2</span></div>
    <div class="box"><span>3</span></div>
    <div class="box"><span>4</span></div>
    <div class="box"><span>5</span></div>
    <div class="box"><span>6</span></div>    
</div>

align-content, align-items and align-self

These properties do the same as their justify-* counterparts, but in the perpendicular direction.

More here: What is the difference between align-items vs. align-content in Grid Layout?

Spec Reference

10.3. Row-axis Alignment: the justify-self and justify-items properties

Grid items can be aligned in the inline dimension by using the justify-self property on the grid item or justify-items property on the grid container.

10.4. Column-axis Alignment: the align-self and align-items properties

Grid items can also be aligned in the block dimension (perpendicular to the inline dimension) by using the align-self property on the grid item or align-items property on the grid container.

10.5. Aligning the Grid: the justify-content and align-content properties

If the grid’s outer edges do not correspond to the grid container’s content edges (for example, if no columns are flex-sized), the grid tracks are aligned within the content box according to the justify-content and align-content properties on the grid container.

^{(emphasis added)}

CSS Box Alignment Module

You wrote:

Is the justify-items property in Flex-box the same as the justify-items property in Grid?

Although the Flex and Grid specs provide their own definitions for keyword alignment properties, such as justify-items and align-content, the W3C is in the process of phasing out alignment properties for individual box models and implementing their new Box Alignment Module, which seeks to define a set of alignment properties for use across all box models.

From the flexbox spec:

1.2. Module interactions

The CSS Box Alignment Module extends and supercedes the definitions of the alignment properties (justify-content, align-items, align-self, align-content) introduced here.

There are similar references in the Grid spec.