Is St. Mary Maggiore the same as St. Maria Maggiore?
 

Is it?

yes

And it is stunningly beautiful with a gold ceiling provided as a gift from Ferdinand and Isabella. They received so much gold back from the New World that they decided to give some of it to the Pope! It was by far one of my favorite churches in Rome.

Isn't this where a piece of the "Last Supper" table is supposed to be?

Got my Churches wrong. The last supper table piece is in the St. John Lateran and supposedly in the St. Maria Maggiore - the crib of Christ covered in gold in supposedly in the crypt under the church. Is this correct?

Santa Maria Maggiore (Italian)
St Mary Major (English)

Yes, the crib is in Santa Maria Maggiore.