What is the difference between alkyd and enamel paint?
You are falsely separating "enamel" and "alkyd", because you can have an alkyd based enamel as well as acrylic based enamel.

Alkyd paint is oil / solvent based paint. Acrylic is water based paint. Some places will not allow you to use alkyd paints any longer because the solvents are VOCs (Volatile Organic Compounds) that are classified as hazardous. Even in areas where not banned, many people who feel they are sensitive to VOCs will not want to use them either, they can out-gas for years after being applied even though you can't smell them any longer. On the other hand many people prefer alkyd based paints because they perceive them as more durable than acrylics. That may be true, but you must also consider that the difference may be 20 years vs 25 years and most people will change colors on something before paint actually wears out.

Enamel is the type of FINISH a paint has, meaning it will be glossy with a hard coat that is resistant to stains or wear and can be easily cleaned. Applying enamel paints of either type is different in that brush strokes will show more in a glossy finish, so you want high quality brushes and you should practice on scraps before doing a final finish if you have never worked with it before. Let it dry in each practice session so you can see the effects of your technique.