Sass is a CSS pre-processor with syntax advancements. Style sheets in the advanced syntax are processed by the program, and turned into regular CSS style sheets. However, they do not extend the CSS standard itself.

CSS variables are supported and can be utilized but not as well as pre-processor variables.

For the difference between SCSS and Sass, this text on the Sass documentation page should answer the question:

The SCSS syntax uses the file extension .scss. With a few small exceptions, it’s a superset of CSS, which means essentially all valid CSS is valid SCSS as well. Because of its similarity to CSS, it’s the easiest syntax to get used to and the most popular.

The indented syntax was Sass’s original syntax, and so it uses the file extension .sass. Because of this extension, it’s sometimes just called “Sass”. The indented syntax supports all the same features as SCSS, but it uses indentation instead of curly braces and semicolons to describe the format of the document.

However, all this works only with the Sass pre-compiler which in the end creates CSS. It is not an extension to the CSS standard itself.

Both Sass and Less are CSS preprocessors.

From keycdn.com

A CSS preprocessor is basically a scripting language that extends CSS and then compiles it into regular CSS.

So Sass and Less don't change the functionality of CSS, as they are compiled into plain old CSS. What they do is make it easier to write and maintain CSS with tools such as mixins, nesting, variables, and more.

SCSS, which stands for 'Sassy CSS' is one of two syntaxes for Sass.
From the sass reference:

The second and older syntax, known as the indented syntax (or sometimes just "Sass"), provides a more concise way of writing CSS.

The difference

Both Sass and Less have very similar features. There are syntactical differences, for example, Sass uses $ for variables whereas less uses @ .
There are some slightly more subjective differences, this website claims that "LESS Has More User-Friendly Documentation Than SCSS", however personally I have found the SCSS documentation and examples very easy to use.

Just to give some examples, because that's often a neat way to explain the difference:

CSS (what the browser understands):

h1.foo {
  background: red;
}
h1.foo .bar {
  text-shadow: 0 1px red;
}

SASS (compiles to CSS, supports things like nesting and variables):

$color: red

h1.foo
  background: $color
  .bar
    text-shadow: 0 1px $color

SCSS (SASS, but written with a CSS-like syntax):

$color: red;

h1.foo {
  background: $color;
  .bar {
    text-shadow: 0 1px $color;
  }
}

The latter two compile to CSS when you run them through a program. You then send the compiled files to the browser, since browsers only understand CSS.