Well, as far as I know there is no difference between a High Commissioner and an Ambassador. They are both important officials who are sent abroad as representatives of their own countries. They are also of the same rank.
The term Ambassador is perhaps the more common of the two. The term High Commissioner, on the other hand, only refers to heads of British diplomatic missions in Commonwealth countries.
At some point in the past the British Empire consisted of many colonies in Asia and Africa. These colonies fought for their freedom and eventually won it. Even after gaining independence, a large number of them continued to be part of an organization called the Commonwealth.
Britain’s diplomatic missions in Commonwealth countries are called High Commissions and the senior diplomat in charge of a High Commission is a High Commissioner.
Countries like the USA, Canada and Russia are not a part of the Commonwealth. Great Britain has diplomatic missions in these countries as well. These offices are called Embassies, not High Commissions. An Ambassador is a person in charge of an Embassy.
For example, the US diplomatic mission in India and other countries are called the US Embassies. In the same way, the Russians diplomatic missions are called Russian Embassies. The British diplomatic missions are called High Commissions in Commonwealth countries and Embassies in other countries