What is the difference between galvanic and alkaline cells?

It's actually "galvanic" and "alkaline" cells, but no matter.

To understand any battery you must first understand the galvanic series, which says that if you take two dissimilar metals and create a conductive path between them, which is called the electrolyte, electricity will flow from one to the other. (The galvanic series was actually invented for sailors so they'd know what metals on their ships would corrode fastest in seawater.) So if you wanted to build a battery that puts out two volts, you'd pick two metals that are two volts apart on the galvanic series.

A galvanic cell has two metals submerged in sulfate solutions of themselves (normally copper in copper sulfate and zinc in zinc sulfate), and a conductive pathway connecting the two containers of sulfate solutions.

Any other kind of battery has the two metals submerged in the same container of electrolyte. An alkaline battery uses a potassium hydroxide paste as its electrolyte.