The reason why you have to register the vehicle to get the title is so the state gets its sales tax.
I suppose the biggest reason why it is different is that gun registration is step number 1 to gun confiscation.
But if you are referring to background checks rather than "registration" then there is currently no apparatus to do it. If you think we should just do all private sales through FFL dealers, then all you are accomplishing is raising the price of every firearm by $50. These high profile mass shootings aside, the overwhelming majority of gun crime is committed with illegal firearms. Absent a registration system, it is also impossible to track compliance with a law that requires all private sales to go through NICS.