What is the difference between a flutter valve and check valve?

Is one more appropriate than another when used with a shallow well pump?

The only "flutter vale" I know of has medical applications . Have you a definition? If so describe how it's used in plumbing. Back to you, Tom

Probably referring to a foot valve.

We are installing a new shallow water pump and one plumber recommended a check valve and the other a "flutter valve" (probably meant foot valve).

Any advantages/disadvantages of one over the other?

You might be referring to what is often called a swing check valve or a gate check valve. It works with a hinged "gate" that swings open to allow flow. A ball check valve, which is linked below, used a ball which lifts to allow flow. I'm not aware that either type has an advantage over the other.

File:Checkvalveopen.png - Wikipedia, the free encyclopedia

jlisenbe called it as a swing check valve, Also there's a spring check valve. In my area a swing check valve's used in the horizontal position while a spring check valve can be installed in the vertical position and is used as a foot valve. Regards, Tom