There are 193 member states in the United Nations. There are other two nations with limited status namely vatican (called Holy See) and palestine with permanent observer status in UN. These two nations arent allowed to cast votes at UN.
There are some nations like Taiwan which is not recognized by China however it is independent. Taiwan is also regarded as Chinese Taipei. Another nation is kosovo which is partially recognized which is actually in dispute with Serbia.
There are some overseas territories/colonies which could have been countries but couldnt govern itself. These are Puerto Rico, Bermuda, Greenland,western sahara etc. Puerto rico is under usa while greeland is under denmark. The United Kingdom retains responsibility for defence and foreign relations for Bermuda. Bermuda is self-governing having its own constitution and government and a Parliament. Western Sahara is disputed which is partially controlled by Sahrawi Arab Democratic Republic while rest by morocco. Morocco is a recognized country while SADR isnt. There are several oversea territories of USA,United kingdom, France etc. Also within uk there are autonomous regions like norther ireland, scotland,wales and england which enjoy some level of autonomy but are under UK as a group. Similar situation you might see in UAE. (united arab emirates).
Ideally we can say there are 196 countries in the world. If we include territories with countries the figure would be around 241. The united nations recognizes 195 sovereign countries with their own 193 members. If we include kosovo and Taiwan then the number comes out to be 197 nations.