The best way to compare and contrast these four things is to say that the first three combine to make the fourth. In other words, courtesy, appearance, and communication skills help to create a first impression. This is the main point of comparison between the four. That said, we can also contrast these because the first three things are all different in important ways.
In business, it is often very important to make a good first impression. That first impression can make or break a new relationship with a customer or with a potential employer. The first three things that you mention in this question help to create your first impression. The other person will immediately notice your appearance. They will notice the degree to which you have taken care to look your best. They will note the extent to which you treat them and others with courtesy. They will notice whether your communications skills are good and whether you are able to put them at ease with those skills. Thus, we can compare the first three things on your list by saying that they are all part of making a first impression.
However, we can also contrast these three things. First, we can say that courtesy and appearance are very different things. Courtesy is (like communication) a behavior. People have much more control over their manners than they do over their appearance. Of course, we can control the sorts of clothes we wear and our grooming. On the other hand, we have much less control over what our bodies and our faces look like. Some of us will always be at a disadvantage in terms of appearance because we do not look as good as other people. Sadly, this is taken into account by most people as they form first impressions of others. Second, we can say that communication skills may be harder to acquire than courtesy. Courtesy is really just a matter of focus and effort. There is nothing particularly difficult about being polite. In contrast, a person can try very hard and still not be a good, effortless communicator. Communication is, to some degree, a talent and a person cannot simply will themselves to be a top-notch communicator.
Courtesy, appearance, and communication all combine to create first impressions. Some of these attributes are harder to come by than others, but they are all important in the business world.
First off, let's define these terms. Courtesy is manner and polite behavior. For example, holding a door open for someone or doing favors for a peer or co-worker. Communication is talking to a group of people about a certain topic such as weather, your day, a project, or ideas you have. Appearance is how you look to yourself or the public. You could look professional, casual, or unkempt, etc. Lastly, a first impression is how someone perceives you when they first see or speak to you.
As for how these relate, I would say that the way you look, speak, and act can all determine how someone will first view you. In a business setting, perhaps in an interview, you are told that the interviewer will have their first impression of you within 30 seconds. When you arrive at an interview you are expected to have a professional, clean appearance. If you were dressed too casual for the occasion, the person may view you as lazy and uncaring. You also are supposed to greet the interviewer by shaking their hand and making eye contact, all while looking confident. Greeting them this way will make you seem courteous and enthusiastic. Finally, the way you speak to them and answer questions will give them an idea of how you will communicate with others. All of these things contribute to business etiquette and the way you should act in a business setting.
I think a good point of comparison here would be along the lines of each of these individual elements as social constructs.
courtesy, appearance and "first impressions" are all obvious social constructs, by this I mean that they are things which are governed by sets of unwritten rules which our parents teach us through simple instruction (eg don't interrupt, don't stare etc.) While communication may seem like more of a practical task or skill it is all heavily weighted by social context. For example there are ways and means of communicating which might be completely appropriate in country a but considered highly rude or simply unprofessional in country b. the same can be said for the elements that make up appearance and first impressions with the desirability of a persons appearance being largely shaped by the situation they are in, a person who may seem very attractive or sharply dressed in one culture may have no appeal in another.
What's most important here is to consider all of these things in a business context as ultimately your question is about business etiquette. With this in mind what might be interesting would be firstly to consider the practical role of each of these things, appearance (dressing appropriate to the situation you are in) courtesy ( showing respect in your business dealings, starting with being conscientious and polite and moving up to a consideration of how you need to tailor your behaviour to different markets) communication ( making sure that you have a presence on the most relevant platforms in order to keep in touch with potential clients or business partners) first impressions (as the previous instructor points out this in pretty much made up of all the other elements, potential business partners will have done their homework on you in today's market and having all of the other elements in place will make a big difference to how they view you )