absolutely not, Devanagari is name of script in which Hindi is written. Devanagari is standard script for writing Sanskrit but it need not be so, in other states of india, people write sanskrit in there mother tongues script. e.g. Bengali, Malayalam, Odiya, etc. also in exams there is option to write Sanskrit paper either in vernacular or in Devanagari(in states other than hindi speaking states)

sanskrit uses devanagari alphabet as hindi. but hindi has some other legaturas as well.