TL;DR:

• If you know the index (the position) on which you'll stop (but NOT include), use slice().
• If you know the length of characters to be extracted, you could use substr(), but that is discouraged as it is deprecated.

Otherwise, read on for a full comparison

Syntax

• string.slice(start,end)
• string.substr(start,length)
• string.substring(start,end)

Note #1: slice()==substring()

What it does?

• slice() extracts parts of a string and returns the extracted parts in a new string.
• substr() extracts parts of a string, beginning at the character at the specified position, and returns the specified number of characters.
• substring() extracts parts of a string and returns the extracted parts in a new string.

Note #2: slice()==substring()

Changes the Original String?

• slice() doesn't
• substr() doesn't
• substring() doesn't

Note #3: slice()==substr()==substring()

Using Negative Numbers as an Argument

• slice() selects characters starting from the end of the string
• substr() selects characters starting from the end of the string
• substring() doesn't perform

Note #4: slice()==substr()

If the First Argument is Greater than the Second

• slice() doesn't perform
• substr() since the Second Argument is NOT a position, but length value, it will perform as usual, with no problems
• substring() will swap the two arguments, and perform as usual

The First Argument

• slice() required; starting Index
• substr() required; starting Index
• substring() required; starting Index

Note #5: slice()==substr()==substring()

The Second Argument

• slice() optional; the position (up to, but not including) where to end the extraction
• substr() optional; the number of characters to extract
• substring() optional; the position (up to, but not including) where to end the extraction

Note #6: slice()==substring()

What if the Second Argument is Omitted?

• slice() selects all characters from the start-position to the end of the string
• substr() selects all characters from the start-position to the end of the string
• substring() selects all characters from the start-position to the end of the string

Note #7: slice()==substr()==substring()

So, you can say that there's a difference between slice() and substr(), while substring() is basically a copy of slice().

If you want substr's functionality:

"foobarbaz".substr(index, length);

without using a deprecated feature, you can just do:

"foobarbaz".substring(index, length + index);

And get the exact same results bar all of the edge-cases, like negative index/length.