Given those choices, the answer would be yes. It's the same material.

What are "shop fittings"?

Shops fittings are like brackets fixed to the wall to display clothing.

Either choice would work, so go with the less expensive. (If corrosion issues were involved, the answer might be different.)

Buy a Machinery Handbook!

Applications From the machinery handbook for 201 SS are flatware and hubcaps because of its high work hardening rate. Less costly than 304. If you want to eat your lunch from a hubcap using a homemade fork this is a good choice.

304 SS is sometimes referred to as food grade and must be used for direct food contact in processing plants. Very high corrosion resistance , precipitation hardening, but weldable. Typical use chemical, food, brewing equipment, downspouts, and flashings. Very expensive also available in drill rod. If you want to make your own brew and urinals this is the SS to use.