SHELL

() vs {} bash

() 
- Placing a list of commands between parentheses causes a subshell environment
to be created, and each of the commands in list to be executed in that subshell.
Since the list is executed in a subshell, variable assignments do not remain 
in effect after the subshell completes.

{}
- Placing a list of commands between curly braces causes the list to be executed
in the current shell context. No subshell is created. The semicolon (or newline)
following list is required.

$() vs `` bash

$() or `` is called command subsitution

They are the same. Command subsitution allows the output of a command to 
replace the command identifier.

$() vs () bash

$(cmd) substitutes the result of cmd as a string, whereas (cmd; cmd) run a list of commands in a subprocess.

If you want to put the output of one or more commands into a variable use the $( cmd ) form.

However if you want to run a number of commands and treat them as a single unit use the () form.

The latter is useful when you want to run a set of commands in the background.