It's true. If you choose tiller your choices are artisan or agriculturalist, if you choose rancher your choices are coopmaster or shepherd. All professions similarly "branch" at 5 and have dependent choices at 10, if you check their wiki page the level 10 options will have a little header above them showing what level 5 option you need to have picked to be able to select them.
Farming is the skill associated with planting, growing, and harvesting crops on the farm, and also the care of farm animals. It's one of the main income sources for the game, and provides most of the ingredients for cooking.
Additionally, it is possible to change post-change. You need to unlock the sewers in town (by donating 60 items to the museum), then there's a statue that will take a 10k payment in order to change.
Since that isn't immediately accessible and takes time for most to get to, picking that initial profession that'll help out early on in your file can be a pretty important decision.