() executes the statements in a new subshell, with separate state. {} executes stuff in the current shell.

Example:

this doesn't print "hello" because the variable was assigned inside a new shell, whose state was discarded when the () expression ended. Think of variable scoping in C; variables live and die inside the block where they're declared.

this prints "hello" because the variable was assigned in the same shell as the next statement.

It's the same difference as:
and


Also, yes, you need a semicolon to end the last statement inside {}; that's how the shell's grammar is defined.
Kind of how you can either do this:
or this, using newlines instead of semicolons to separate the syntax parts:
According to the bash man page, it's different from () because { and } are reserved words instead of metacharacters, which means they don't automatically cause word breaks. Presumably the same applies in the rest of the shells.