They both mean the same thing technically. But neither are used really since they seen as offensive. The correct term is speech impaired.

It's almost the same meaning but those words are offensive so be careful. :)

Personally, I don't regard "mute" as being offensive. "Speech impared doesn't necessarily mean that someone is unable to speak; it just means there is some sort of difficulty (i.e. a stutter, etc)

These are offensive words, or that is how they are perceived. But they mean the same thing.