Many definitions at other places place solipsism as a philosophy and narcissism as a disorder. Aren't both the same ? And where does egoism fit in with solipsism ?
I'm foregoing standard definitions as these can be Googled easily and your focus is on the difference between the three (actually four), rather than a definition for all three.
- A solipsist thinks he is alone. Whether that means he is truly the only living creature, or he is the only living creature that matters (e.g. the only person capable of doing something), is irrelevant. However, in most cases, you will see this used for people who (wrongly) think they are unique.
- An egotist has a inflated sense of self worth. They do not think they are the only person. However, they do think that they are the best person. This can be faked (pretending you're better than others while you realize you are not), or honest (actually thinking you're better than others)
- An egoist is actually slightly different from an egotist. Egoists only think about themselves, but do not necessarily think they are better than others. It's just that they consider themselves more relevant to themselves.
- A narcissist is somewhat related to an ego(t)ist. However, depending on who you ask, narcissism is considered a mild version of mental illness. This isn't a matter of actively thinking you're better than anyone else; it's a matter of being psychologically incapable of seeing anyone else's point of view or empathize with anything that is not in your favor.
Some overly simplified examples:
If I got fired from the company, all the work would stop.
That's a solipsist.
If I got fired from the company, the quality of work would become pathetic.
That's an egotist.
If I got fired from the company, what will happen to me?
That's an egoist. Their approach isn't particularly wrong, it's just almost always revolving around them (their future) as opposed to someone else (the company's future).
If I got fired from the company, then it must be because they envy my skills.
That's a narcissist. They honestly believe that their way is beyond reproach, and cannot fathom a reality in which they deserved to be fired. They will resort to twisting reality itself, before they even consider admitting personal flaws.
Admitting personal flaws, from close personal experience, is something a narcissist will never do. I have browsed many communities of people affected by the behavior of narcissists, and it is a recurring theme that the narcissists (quite often parents) would rather will someone (their child) out of existence before acknowledging being wrong.
You could argue that a narcissist is a compulsive ego(t)ist.