I may have some of the terminology wrong (but I think they are also using it sloppily?) but that's the basic idea yeah. The "captains list" is the officers eligible to be posted in the role of captain of a ship, which is not quite the same as the rank of captain.
Officers with the actual rank of captain would normally be permanently posted to a ship's command, and only large, prominent, or prestigious warships were captained by captain-rank officers. So it was highly desirable to at least attain that rank. You could get there by achievement on a temporary command which is part of why they were so sought after. Or simply through politics and patronage: the naval officer corps being intimately tied up with both the waning aristocratic and emerging modern nation-state systems.
Officers on the lists were necessarily "gentlemen" in a technical legal-social sense, and were mostly free to pursue their social, family and business interests when not posted to a command. Depending on their resources and connections outside the navy, they could have quite excellent alternatives to a command that was unlikely to make them much money. Or, like younger sons of small or declining holdings would take anything they could get.
Anyway this is what I remember from all the external reading I did trying to make sense of the politics of command in the aubrey-maturin books which is I think the normal way to learn it these days.