Honorable discharge (from the military) means you completed your contracted tour of duty without any major issues. It's not a meritorious distinction, per se, as it is what you get when you do what is expected of you.
Medical discharge (or separation) is as the name implies. Some medical condition now impedes their ability to serve their contract.
Administrative separation is a very broad category, but effectively means that military has opted to dismiss someone from their contract. It is almost always a bad thing - discipline issues, violating policies, not complying with standards….
Dishonorable discharge means you have jail time waiting for you, and not for failing to pay a parking ticket. I can think of very few people who have been dishonorably discharged without serving time in jail.
Even going AWOL or deserting usually results in an administrative separation, because a dishonorable discharge has reaching implications for a person outside the military.