No, that statement is not true. I could explain it, but I'll say that there are very good explanations for all of these if you do a little more googling. I'd encourage you to try, because you'll find some great info along the way.
For a brief brief summary:
401k (either roth or traditional) and 403b are employee sponsored retirement plans. 401k and 403b are similar (maybe even exactly the same) except 403b are only offered to certain types of (public?) employees.
IRA is an individual retirement account, not through an employer.
Roth vs Traditional there are 10 million threads here and elsewhere to explain the differences and the pros and cons.
Good luck!
There is a boatload of great info here and elsewhere if you are up for the search.
Cheers,
James