When I have a problem after purchasing something at the store, I'd like to take it back to the store and change it. These are two examples. One is that I bought a rug, but it didn't fit the space, so I'd like to change it to something different. Another is that I bought a space heater, but there's something wrong, so I wanted to change it to a different one. In these situations, which verb shoud I use? Or can I use all three verbs interchangeably, saying "I'd like to replace / exchange / change this." or "Could you replace / exchange / change this?" I looked up the differences on the internet or the dictionary, but still I cannot get it.
You want to exchange the item you purchased. That is, you want to return to the store the one you bought and have the store give you a new one for one reason or another.
You want the store to replace it.
The clearest way to express this in American English is to say to the salesperson or service desk person:
I'd like to exchange this rug for a larger one (because it's too small for the space I want to put it in). [NB: The reason is optional unless you're asked for a reason.]
I'd like to exchange this space heater for a new one that works. When I tried to use this one that I bought here yesterday, it didn't work. Can we test the new one here before I take it home?