One could argue that Apple Computer is not involved in the production, labeling or promotion of music, as Apple Corps is, but rather only in distribution and sales which Apple Corps does not do. However I don't think that there are separate trademark categories for these 2 different hazy differences in the music business.
The specifics of a trademark infringement are not clear cut and so taking it to court might be necessary if the 2 parties can't come to an agreement.
The fact that Apple and Apple have a legal agreement about they they can and can't do makes it even more interesting. It's not like Apple Computer doesn't have a huge legal department. They didn't do this without getting legal advise with full knowledge of all the previous things going in. They obviously decided it was not going to be a problem. We know that both parties talked to each other and were unable to come to an agreement so far which is why they are all threatening to go to court. We don't know what was offered or went back and forth. Usually companies are fairly reasonable when negotiating in good faith back and forth, but it's entirely possible that the only option Apple Corps offered Apple Computer was to drop it and go home. Which obviously they aren't going to agree to do, it's too lucrative for them.
I expect we'll never know all the details of what was accused and what was agreed to only that eventually they will all go home happy and some money will change hands. Historically the pay offs to Apple Corps have been well worth the money to Apple Computer as they have been measured in the millions and I'd guess just considered a cost of doing business. In all the cases previous Apple has gotten to continue to do what they wanted. It will be interesting to see what happens!
As far as other companies copying the Apple 2 and the Mac, thats more complicated. Several companies DID clone the Apple 2. Some of them with Apple's blessing. In Europe a company called "Europlus" made one in a slightly different case and had Apple's permission to do so. There was another American company that did too, but I can't remember who it was. I used one in a programming class I took so many years ago I can't remember anything else about it. But it was not an Apple.
The Mac did something unusual, in that in addition to a simple bios they also burned a significant amount of the system libraries into ROM and placed this on the motherboard. Reverse engineering a simple bios like they did to clone a PC is a tiny project compared to trying to do an entire operating system library. They owned the copyright on this code and anybody that wanted to clone the Mac had to basically pirate it. Apple succeeded in court where IBM failed in defending their bios. One could argue that it was not the brightest thing Apple ever did to stop the clone makers, but you can't fault them for the legal action. It was all standard business practice and nothing evil.