Frontier and Standard are two different formats. Standard (also called Type II) is the latest blocks of cards, and usually involves dropping a block when a new one is released (this won't happen with amonkhet for various reasons.) The current Standard blocks are Battle for Zendikar, Shadows over Innistrad and Kaladesh.
Frontier is a format that has a beginning point that doesn't change, but all new sets are added to the format. The beginning set for Frontier is M15. Everything after that is allowed in Frontier.
Modern is like frontier, but the
cut off set is much older. Eighth Edition (and all its white bordered goodness) and after are legal in Modern.