No, the number gives size if you remove the end zero.

Thus, 18650 are 18mm X 65mm

20700 are 20mm X 70mm

21700 are 21mm X 70mm

Big deal about the larger sizes is capacity and max safe discharge rate

Capacity tends to be inversely proportional to discharge rate. Example, highest capacity 18650 (quality manufacture not dubious) at this time is 3500 mAh , or 3.5 ampere hours, which has a safe discharge rate of 10 amps.

20700 are rated at 4250 mAh, but average tested capacity is more like 4000 mAh, however they support a discharge of up to 15 amps.

21700 is something I have not yet used or looked into, but a quick search reveals Nitecore, which is probably a rebrand of a quality OEM, at 5000 mAh and a safe discharge rate of 5 amps.

Notes

1/Quality manufacture, typically Sanyo or Panasonic against "BangFire" or whatever.

2/Earlier Sanyo 3500 mAh cells were rated at 8 amps

3/Chemistry denoted in type legend. example, latest 18650 is NCR 18650GA. "NCR" = Nickel Cobalt Rechargeable.

This probably more than answers your question, typical me, sorry.