to elaborate on what GreenLED said.....
Some protected cells have very basic current limits set on them... If the cells were intended to be used in slow drain applications like a laptop or LED light, then there may or may not be a very high current threshold... For example: I bought some 17500 size cells awhile back from a source I won't mentioned at this time... they are great cells that live up to their capacity rating very well, however, they will not deliver any more than about 1.3amp without going open circuit... good for LED lights, terrible for incandescent lights...
Then there are cells like the ones Wolf-Eyes, Pila, And AW (dealer section) sell.. these are protected cells, that have higher than normal current limit settings... In some cases, the protection circuit is actually set to allow current higher than would actually be safe for continual discharge of the cells... This is done so that these cells can light up big superbulbs that have an initial "current spike" while the filament warms up(all bulbs have this behavior, but the bigger the filament, the bigger the current spike)- Of course, it becomes the users responsibility to choose a load that is appropriate for the cells. The protection circuits in cells like this are there more to prevent short circuit conditions, and overcharge/discharge.
[edit in] then of course, there are time bombs I call unprotected cells...
Well... actually.. as long as the user is careful never to short circuit these or work them way too hard, there is a good chance there will never be incident.. The trouble is when they are discharged too far, the discharging too much goes smoothly. but then the unsuspecting user puts the over-discharged cells on the charger, and a few hours later, the living room is filled with toxic gases and chemical fire.