High commission and Embassy no longer exist. An embassy is a diplomatic mission of a country delivered to a non-commonwealth country. On the other hand, an Embassy also possesses the building where the diplomats work or live. The person linked with the Embassy is called an ambassador.
An embassy is the formal representation of a country in the capital, and there are different staff in the Embassy with various tasks. An embassy investigates concerns relating to Visa and travel issues. India is an example of an Embassy.
However, the high commission is a diplomatic representation between commonwealth countries. When it comes to responsibilities, high commission deals with the task of carrying the mission of one commonwealth country to another. A high commissioner is a person who maintains high ranking positions, including executive positions approved by the commission of appointment.
The two primary officers of a high commission include Governor and Governor-General.