It drains to a trickle and then continues indefinitely. The supply is less than bitcoins until 2040.
Still, like Bitcoin, the vast majority of all Monero emitted in the first century, is emitted in the first few years.
Grin has the simplest possible emission, at 1 Grin per second forever. They're all disinflationary, i.e. the yearly inflation rate goes down to 0.