The core difference is that:
- `[` is treated as a statement
- `[[` is treated as an expression
Which, for example, is why you can't use `>` in `[` based expressions. Bash thinks you want to redirect the output of `[` to somewhere else. This restriction is lifted for `[[` and makes for much more natural looking code.
That's because '[[' is a special bash extension which started out as a better '[' which is actually a binary (/usr/bin/[). And, well, you have to have a space between an executable and its first argument.
(nowadays '[' and '[[' are builtins in most shells, but the external binary still exists).