I prefer the term "current limit" rather than "constant current".
You can prefer what you want, but the problem with term "current limit" is that there area many different ways to implement it: constant current behavior, or latching "overcurrent fault" mode, for example.
Constant current describes the behavior where current is actively regulated to be exactly at the setpoint. "Current limitation"
often implies something more crude, like protection: inaccurate, time-limited CC, foldback limiting, hickup mode, latching fault mode until reset, and so on.
Your logic that constant current operation cannot be achieved with 1M ohm resistor is broken, because by the very same logic you could not talk about constant voltage supplies either because they would fail to deliver constant voltage into 1ยต ohm resistor. Yet we all talk about constant voltage supplies all the time.
Hence, ignoring products that just blow up, realistic power supplies are one of the three classes:
Constant voltage with current limit - behavior of current limit can be anything, including shut-down. Typical example: wall-wart or PC PSU
Constant current with voltage limit - behavior of voltage limit can be anything, including shut-down. Typical example: LED PSU
CC-CV supply: behavior is well defined, at any point in time either CC or CV applies, whichever is the limiting factor. Of course you can't call it just CC supply, because it has CV, too. It has to be CC-CV; if not, it's one of the previous two types. Typical example: lab PSU.
Calling a lab supply "constant voltage + current limit" will only cause endless confusion. "Voltage limit + current limit" is a tad better because no one says that and it forces the listener to check up what the heck you are talking about.