What I’ve gathered form my 1.5 years of experience is that the labels have to do with you number of hives and intent and the law in your area is written.
A hobbyist / armature / “backyard Bee Keeper” (me) just does it for kicks/honey/"save the bees" etc. You only have a few hives. In my city it's less than 10. This group tends to keep the catalog companies in business.
A side-liner is supplementing their income with the bees. Selling to friends, neighbors and at farmers markets etc. where they sell enough to cover the cost of the equipment and a little left over for beer money (or so the IRS knows). In my area this is anyone with greater than 10 hives but less the 300. (If you have just 10 hives, it’s unclear where you fall).
And professionals are the guys that do it for a living. This is the category where your IRS statement has “Bee Keeper” (or is that Apiarist) down for your profession. They haul the bees from one end of the country to another doing their part to keep the rest of us fed. The term “live stock” comes into play here instead of “the girls in the back yard”.
And a I like the idea of a bee keeper being anyone who has kept a hive alive over a winter (you’ve got to prove your stuff).
Well, I feel like an empty barrel here, just rattling on, but it’s slow here at work and I wanted to through in my 2 cents.