You can come along for the ride too. Correct me where you will.
High Commission: An embassy of one British Commonwealth country to another, normally in the country's capital city. So for us in Australia, that would be Canberra. We would have a High Commission in London and say Wellington in New Zealand. God save the red bits on the globe.
Embassy: A diplomatic mission in the capital city of a foreign country. Same as above. Embassies in Canberra. We would have an Embassy in Washington and Paris.
Consulate: A branch of an embassy or high commission found in major cities. So we have high commissions and embassies in Canberra and consulates in big cities such as Sydney and Melbourne. I expect we would have a Consulate in New York.
Ambassador: A diplomat of the highest rank. So he or she would be in Canberra. We would have an Ambassador to the United States or to France.
High Commissioner: He or she would be the same as an Ambassador but in Commonwealth countries. High Commissioner in London. High Commissioner in New Delhi.
Consul or Consul General: A senior diplomat at a consulate. Consul General would be the senior diplomat at a consulate.
Did I leave anything out? And no, I am not adding the self explanatory honorary consul or the lord high commissioner.