The New Mutants were a group of young mutants taught and trained by Professor Xavier to someday become X-Men.
The first X-Force team was formed in 1991 as a spinoff from another X-Men series, The New Mutants (which is also in the process of being turned into a movie by Fox).
(The guy in the back has a great mustache, but I’m not familiar with any X-Force members with super mustache powers.)
If you don’t know an X-Force from an X chromosome, here are all the important details.