well, yes and no.
sniper1 is actually a marker made by WGP back in the 90s (i think)
they made sniper 2 and 3 as well and there were different variations of each.
they were a pump action version of a standard autococker.
more recently, Empire brought the name back for their 'cocker based marker. thats what youll see in this section of the forum more often than not.
what i believe you are referencing when you say sniper is more of the mil-sim type of marker with a long barrel, some sort of scope or sight and all sorts of accessories attached. while these markers look pretty cool, they are not any more "accurate" than any other marker, nor do they shoot farther or at higher velocities.
there ARE markers that are mag fed that can utilize the pretty cool "first strike" round, which is a fin stabilized paintball. theyre still .68 caliber but instead of a sphere, they have a half sphere shape up front and fins on the back half that can actually engage rifling in barrels. these are FAR more accurate and, because of their design, farther shooting than standard paintball. the first strike rounds are also FAR more expensive.
there are several first strike capable markers. some are pistols, some are smaller "SMG" styled markers and in the highest end of the market, bolt action, long barrel "sniper rifles".
this isnt my normal style of play so i cant really answer many more questions about it.
long story short, pumps are called snipers because of the marker WGP made back in the day. pump markers are called snipers because us pump guys think were super cool.
good question, though. welcome to paintball!
if you have more questions, there are other area of this forum that are more dedicated to chatting and questions that can be found
here and more specific to your original question
here