There isn't a difference which is why you aren't finding any. A catch basin is a type of "area drain". It gets a bit confusing because they use the word "drain" to talk about both physical 'drains' and types of 'drainage'. A catch basin is a type of drain, while 'area drainage' is the draining of an area to a point or to an 'area drain' such as a catch basin.
NDS is a drain manufacturer that I specify all the time, and they have this great document which has a ton of good information in it. Covers info that would be useful for Section 3 and 4 of the LARE. Link is here:
Pages 13-19 have some good info on types of drains and Page 23-24 talk about types of drainage (including directional drainage or draining to an area drain)