what is difference between embassy and high commission?

Countries which are members of British commonwealth , their Representative office in other member country is called High Commission.

(British commonwealth is association of 52 countries which were ruled by British Empire)

Countries which are not members of British Commonwealth have embassies in other countries.

head of embassy is called ambassador and head of high commission is called high commissioner

to make it easy i will give you example

Canada and Pakistan both were British colonies and they are members of British Commonwealth , So Canada have High commission in Islamabad and Pakistan have High commission in Ottawa.

But in Case of USA (who is not member of British Comment wealth) have their embassy in Islamabad and Pakistan have it's embassy in Washington DC.