I won't bother going into the differences, mostly because I don't care that much. I think what's important is that you are comfortable and enjoy your ride.
As far as a new bike, you might want to give the folks at your local bike shop a shot a making fixes on what you have.
With the bike I usually use, I rode it for about 3 months and started really disliking a couple of its aspects. I went to the same shop and asked the guys if they could help me do something about the issues to make the ride more tolerable until I had saved the money for and located the bike I *really* wanted. Sure enough, I got a new seat and a new stem. This made a world of difference.
Also, just this week I got a '69 schwinn I've been keeping around for years back from the shop. The guys cleaned it up nice and put on new tires, fixed the brakes and all that. So, for a very reasonable price I had yet another way to have fun on two wheels.
Welcome to the club.