1. They are all 3-volt lithium
The CR1632, CR1620 and CR2016 are all lithium manganese cells that give 3 volts, the same as a CR2032. They keep their charge for about 10 years on the shelf and work down to about -30 °C.
2. The 16 mm ones are narrower
A CR1632 is 16 mm across and 3.2 mm thick, and a CR1620 is the same 16 mm across but only 2 mm thick. These are the classic cells for trackers and small key fobs, and they will not drop into a 20 mm slot.
3. The CR2016 is thin rather than small
A CR2016 is the full 20 mm across but only 1.6 mm thick. It fits slim watches and thin remotes where a CR2032 is too tall to close the case.
4. Smaller means less capacity
A CR2032 holds about 225 mAh, a CR1632 about 137 mAh and a CR2016 about 90 mAh. More mAh means longer between changes, but only when the voltage matches as well.
5. How to tell them apart in a drawer
Read the code. If it has worn off, measure the width and the thickness, or hold the new cell against the one you are replacing. The width is the giveaway: 16 mm or 20 mm.