Actually, a snipe is a small, very fast bird. Those shootists who were able to make consist kills on snipes where called "snipers". Ultimately, the terms was adopted for military personnel who were adept at hitting humanoid targets. The first sniper rifles did not necessarily have heavy barrels. These first snipers were typical farm-boys and others riflemen. Later, formal training was created, dropped from the military and recreated. Becoming a sniper has been a pretty hap-hazard process until fairly recent history (compared to the age of the USA).
There is an old saying, "You are what you do, and you do as you choose to do." I am a shootist, perhaps a rifleman or marksman. I have never sniped at anyone. For my likes, I wouldn't want a sniper rifle. A target rifle would be nice, even settle for a varmint rifle if I had to. Don't have any desire for a sniper rifle. IMHO, you have a fine hunting rifle that if you practice enough would be a fine hunting arm, perhaps even capable of an Appleseed shoot to qualify as rifleman.
