The old style backticks ` ` and the $( ) constructions do the same thing, but treat the backslashes different.
Using backticks:
$ echo `echo test`
test
Using $( ):
$ echo $(echo test)
test
In the $( ) construction, everything in between ( ) is interpreted as a command.
As we can notice, the two tricks behave different when interpreting special characters:
With $( ):
$ echo $(echo '\\')
\\
With backticks:
echo `echo '\\'`
\
In the second construction, the “backslash” \ escapes the second one, while in the first, the sell interprets it as normal character an prints two “backslashes” \\ .
I avoid using the backticks, because they can easily be confused with the normal ticks ‘ ‘.
All the new shells support both the ` ` and %( ) constructions. The old bash does not know how to interpret the $( ) trick.