US phraseology is:
Bugsplasher 123, descent and maintain FLxxx = Start your descent promptly and follow minimum vertical speeds for your aircraft kind (500 fpm for piston, 1000fpm for jets).
Bugsplasher 123, pilot's discretion descent and maintain FLxxx = There's no conflicting traffic so you can wait until reaching your optimal top of descent based on your final destination (or crossing restrictions further ahead on a STAR) and off you go
Bugsplasher 123, cross XPTOZ at FLxxx = You need to be at FLxxx when you get to XPTOZ, but you can wait as long as you'd like, as long as you are at FLxxx when you cross XPTOZ, also means no conflicting traffic until FLxxx, typically that intersection will be the handoff point between CENTER and TRACON.
There's also cross yyy miles north/south/east/west of XPTOZ at FLxxx = Create a virtual waypoint offsetting XPTOZ by yyy miles and comply with that.
Either case, in the USA case, under radar surveilance, you only need to readback the clearance, but don't need to report starting your descent if it happens later.
In case you are not under radar contact, the leaving altitude phraseology is mandatory. The training materials (AIM) teach us to say leaving xxx for yyy in all cases, but ATC doesn't expect, nor want that information when under radar coverage.