Hello everyone!
I've been searching around the forum for a while for a solution to my particular issue but haven't found anything. I don't know much about bikes but have been trying to educate myself...

I have a Schwinn mountain bike and I need to replace its rear derailleur. It came with a Shimano Tourney RD-TX51. I haven't been able to find it online and have found the Shimano Tourney TX55 and the Shimano Tourney TX75 online. I assume the TX51 that originally came on the bike has been discontinued.

I've looked up the specs for the TX51 that came on the bike originally on the Shimano site and have been trying to find a match for it using the specs of the TX55 and TX75 but haven't been able to do so. The Shimano site doesn't list the detailed specs of the TX55 and TX75 on their site like they did for the TX51's.

I believe that the new (TX55 and TX75) derailleurs don't have as long a cage as the old TX51 I have. Would that make a difference?

Amazon's info on the TX55 says that it has:
Longest Cog: 34 teeth
Chain Wrap Capacity: 43 teeth

These two numbers match the information on the original TX51's information sheet on Shimano's site:
Rear largest sprocket: 28-34T
Total Capacity: 43T

I assume I'm looking at the same information about both.

So the question is which derailer can I buy? What information should I be looking for when trying to find a replacement?

I don't need anything fancy, I just use the bike to go to school and back, 4 mile commute every day. And what it came with originally sufficed me very well.

Thank you for any assistance you can provide!

The question is

What is the total capacity that you have on your bike and what size is the rear sprocket largest cog?

Looks like you found an exact match. Go for it! If you get it from Amazon or a reputable online retailer, just be sure they take returns if you don't like the TX55.

Also make sure that if your bike requires a mounting claw, that the derailer comes with a compatible one. The old one may not be compatible with a newer version of derailer, even if they both are called Tourney.

^^^^^
The Tourney derailleur comes both ways (with and without the hanger "claw") so be sure you get whichever one matches what your bike had before.