Is a mushroom dashi and different than a typical dashi?

A Dashi is a style of Japanese stock or broth. Much like chicken stock, fish stock, beef stock, etc. the stock can be altered by the inclusion of a key ingredient. So your mushroom dashi will be heavy on the mushroom taste-not sure it will benefit your chowdah!
Momofuku's David Chan makes "Bacon Dashi". It's a mother stock at his restaurants, and to make a batch, he uses a pound of Benton's Bacon! For a stock!
I'd grab a basic recipe and make my own Dashi, it's simple to make and freezes well.

And for future reference, it's easy to make your own dashi! https://food52.com/blog/9800-how-to-make-dashi

First...I'd love to have that recipe. Do you have a link? :)

It depends on the ingredients. Does it contain bonito flakes and kelp? If it's straight mushroom dashi (usually shiitake) it is usually used with another seafood dashi. You could use bottled clam juice and the mushroom dashi.