Take Randall Gay, for example, who recently joined the Saints after four seasons in New England with the Patriots. According to this article, "learning the Saints defensive terminology has been the biggest challenge for Gay."
For some coaches, the more complex the terminology, the better, as it makes it harder for opponents to scout your team. On the other hand, if you have a big playbook, you need the play-call system to be easy to understand, with wording that's easy to remember so players can react instead of overthinking.
As a coach in the CBA, where rosters change frequently (in a 56-game season, we once had over 60 players on the roster) I learned quickly the importance of terminology and having sets correlate with terminology.
As a kid, I'd watch my Dad's teams and study their terminology. To learn it, I tried to put it in terms that were easy for me to understand and remember.
In college, I loved talking with guys on the football and baseball teams about terminology they used. Over time, I've borrowed terms from different sports that are easy to learn.
For example, our "no layup" rule was called "sack" as in "sack the QB." Terms for our presses all originated from NFL defensive terms. We had our late game or "2-minute offense." All pick-n-rolls, no matter where on floor or out of what set, were called "fist."
For all double-screens, we had one simple phrase: "Red." "50," "suicide squeeze," and "Hail Mary" -- all terms borrowed from other contexts.
This summer, I helped my son and his AAU team come up with easy-to-remember terms. I also had weekly lunches/dinners with some of the St. Mary's and local high school coaches. And I had the chance to sit down recently with Oakland Raiders QB coach John DeFilippo where we talked about about play-call names. QB coaches like John are a great resource, especially when they're dealing with a young QB who is learning a new system.
On a coaching staff, guys bring with them terms and phrases from their previous jobs and teams. On occasion, we'll create our own for the play or situation. Regardless, I feel the best terms are (1) short, (2) descriptive, and (3) memorable or associative.