Depends. If you have an older 270 rifle its most likely chambered in 270 Winchester and that ammunition will work.
Your rifle could be chambered in 270 WSM (Winchester Short Magnum) if it was made after 2002.
I don't believe you can chamber either round in the wrong gun. The 270 Winchester is too long to fit in a 270 WSM and the 270 WSM is too "fat" to fit in the chamber of a 270 Winchester.