If you use a charger dedicated to Li-ion batteries it will stop charging once the battery is full, since Li-ion batteries can overheat if you keep (trickle) chargeing it once the battery is full.
Older chargers will switch to trickle charging to compensate for the self-discharge of the battery. Li-ion batteries do show self-discharge, but much less than older battery types, say 1-2% per month.
That can be harmful to the battery if you leave it lying around for a longer time almost empty. A friend of mine couldn't charge her gear S3 anymore after not using her watch for months. Apparently, Li-ion batteries don't like being stored fully charged either, so if you plan to not use your watch or phone for a longer time it's best to charge it to say 50% and then leave it.
I got the info from this highly recommended article:
https://batteryuniversity.com/learn/article/how_to_prolong_lithium_based_batteries
The interesting question is if the battery is actually full from a battery point of view if your charger light turns green. It probably isn't. Li-ion batteries are "calibrated" using a built in battery management system, which will indicate the battery is full or empty (100% over 0%) while it really isn't to prevent the battery from getting damaged.