what do you mean by "ordinary PSUs"? Most are cc/cv, exactly like chargers are...ie they will do a constant current until they hit a certain voltage and start tapering current off to remain at said voltage.
"Most" PSUs are not cc/cv; it's much more typical for them to shutdown upon overcurrent (if they have any safeties) or just fail (if they don't). Generally only specific PSUs intended to run LEDs, or other specific uses that require CC/CV operation, will have it, because it is a more complex (and more expensive) design to implement, and generally no more money will be spent on creating something than can be gotten away with.
The primary difference between chargers and cc/cv psus is that a properly designed charger has a circuit to detect when current drops below some tiny limit, and turn off or disconnect it's output, while a psu does not--it will always output whatever current that the load will draw.
Some, like the Grin Satiator, have that limit as user-programmable (per-profile in it's case).
A typical cc/cv psu does not ever turn off; it continues to output voltage even if no current were flowing. In a battery charging scenario, this means that if left by itself, it will continue to trickle charge the cells "forever", which has the potential to damage them over time. You can put a fine-reading ammeter in series with the charger/battery connection to see this happening.
If the pack has a properly designed and manufactured BMS (many are neither), it will disconnect it's charge input from the charger once any of the cells reach the voltage programmed into it as "full", so it doesn't matter if the charger stops or not. ****
If there is no BMS, or if it isn't properly designed or manufactured, or is damaged or bypassed, (all of which appear to be relatively common issues in posts here), the pack will continue to be charged even after it is full, albeit with a very tiny current.
**** but most BMS use FETs for the disconnect switches, and most of them have some amount of leakage current even when "off", so depending on the BMS design and part choices and system voltages, it may not actually turn off the charge input as far as this situation is concerned.
