Why the count changes from quiz to quiz
The one number with a precise definition is 193: the member states of the United Nations. Add the two non-member observer states — the Holy See and the State of Palestine — and you get 195, which is where most published lists stop.
Beyond that it is genuinely contested. Taiwan is governed independently but is not a UN member. Kosovo is recognised by many states and not by others. Western Sahara's status is unresolved. Depending on which of these a quiz includes, its total lands anywhere from 193 to about 197 — and every one of those totals can be defended, which is exactly why a quiz should say which it chose rather than marking you wrong from an unstated list.
This matters more than it sounds. If a quiz counts 196 and you learned 195, you will lose points on a question about a place whose status is a live diplomatic dispute, not a fact you failed to learn.