How can I tell if I have a standard well tank

A "standard" well tank, also known sometimes as a pressure tank is just a tank and is usually galvanized to prevent rust. It is just a sealed tank with fittings for pipes.
A bladder tank is a tank with bladder inside, usually made of some kind of rubber. The bladder is like a balloon inside the tank. These are usually painted on the outside to prevent rust. The inside is usually treated to prevent rust. The bladder tank will have a valve stem (just like a car tire) to inflate the bladder.

The Widget Maker nailed it with this explanation. Here are pictures of both. Regards, Tom