Yes, the proofs of ownership needed to register and title a vehicle in New York are different for different types of vehicles for example cars, trailers, boats, snowmobiles, manufactured homes.
Regarding entering my full address in the New York State Registry for Out-of-State Snowmobile Transactions, can I use abbreviations in the address?
If the street name is a word which has an accepted abbreviation use that abbreviation.  You can also abbreviate the street type or just leave it out.
Is it necessary for me to bring the dealer's bill of sale to show that I paid the NY State sales tax?