All vicars are priests (as are bishops and curates) because a priest is the term for someone who has been ordained as such (although I think the CofE's use of "priest" normally refers to people below the rank of bishop). The incumbent of a parish is not always known as the "vicar", though. If you go back to the time when the population had to pay a tithe (10% of their income) to the Church, the person who was entitled to receive this was termed the "rector". The incumbent was only the "vicar" if someone else received the tithe.
You still see cases in the paper where a person (not a priest) owns a particular house or piece of land and this ownership makes them the "lay rector" of the local church - they don't get paid a tithe any more, as it's been abolished, but they still have a legal responsibility to maintain the church building.