Well, 18650 and 18350 are battery sizes, not really 'types'. The first 2 numerals are the diameter, the next 2 are the length and the last is the battery shape. An 18650 is 18mm diameter, 65mm long and is round (cylindrical). There are also 18500, 16xxx, 14xxx and I believe 10xxx used for vaping.
Battery types for me refers to chemistry used. IMR, ICR, hybrid and LiPo are all used for vaping. ICR are typically protected, the rest are typically not but can be also. A couple of other types are used too, but not often.