Are blackfeet and blackfoot the same tribe?

Yes, "Blackfeet" and "Blackfoot" refer to the same tribe.

Usually. If you are asking about the Siksika, the Algonquin-speaking tribe of what is now Montana and Alberta, then yes.

There is a sub-tribe (band) of the Dakota (Sioux) who were also called the Blackfeet.

Anyway, the tribe in Montana call themselves the Blackfeet, while the same tribe living in Canada is usually referred to as the "Blackfoot".

For references to more detailed sources of information on the name of the tribe(s) (there are actually three tribes in the Blackfeet/Blackfoot confederation), see The Blackfeet: An Annotated Bibliography by Bryan R. Johnson.