So you want to know about Covers!
You are correct about there being two ways covers come into being.
Soul Pact - This option is the more intense way to gain a cover. A demon (Let's call him Bob) makes a pact with a person (Let's call her Sue), Sue gets certain benefits, and Bob has the chance to gain a new cover if need be. When Bob calls in the soul pact, he kicks Sue out of their existence and takes over. As far as everything is concerned Bob is and always was Sue. So, in that cover, Bob is now a woman named Sue.
Patchwork cover - This option consists of building your cover piece by piece. Say, for example, that Sue had been bit by a dog when she was a child and has a scar on her left arm as a result. Bob might offer to trade that dog attack for, say, a new fur coat. If Sue accepts the deal, everything related to the dog attack no longer applies to her. It applies to Bob's cover. Suddenly, everyone KNOWS that Bob was attacked by a dog as a child. Look! There's the scar from it on his arm! He went through years of therapy because of it! That dog remembers biting Bob. Sue's friends remember seeing Bob get bit by the dog. Sue remembers that she was the one bit, but if she tries to argue the point, everyone will assume she's crazy and hurtful for trying to deny that poor Bob went through that traumatic experience.
So! to address your question about the physical appearance of a demon... It depends on the nature of the change to the cover. If it is a physical change (like the scar), then the demon's physical appearance will change. If it is a mental change (like the new fear of dogs), then his physical appearance will not change. If it is a called-in soul pact, his current cover does not change. He does, however, gain an additional cover that does have a different appearance from the original cover (unless the new cover is the identical twin of the old cover... but at this point things are getting weird).
Oh, and regarding whether a non-soul pact is a partial soul pact... No. The soul does not get involved unless it is a full soul pact. What is happening in a regular pact is that you are signing away a part of Reality itself. You had claim to it, and now you have given it up to be rewritten.