Name of buddhism in Sanskrit

[jeraru]

Hello. I'm searching for the word that means "buddhism" in Sanskrit language. I've founded three: बुद्धधर्म buddhadhárma, बौद्धदर्शनम् bauddhadarzanam and buddhaśāsana. I read in the internet that the term buddhaśāsana, in his pali language version: buddhasāsana, is used nowadays in southeast asia. I have a few questions at this respect. There is a word of them that is a neologism? Is there a word that is more used than another or an "official" word? Is there a word that is more used in some regions of Asia than another word? Is there an appropiate word in use in the age of widespread of buddhism to the concretely region of ancient China and Japan that maintains in use in the liturgical Sanskrit of their respective schools of buddhism? and finally, is there a some kind of difference between the word buddha and bauddha?

 

Thank you.