[frederikvs]

In e.g. a monarchy, the head of state is the king or queen. In many monarchies these days, this person tends to have very little actual power.

The leader of a country is the person leading it, e.g. a president, prime minister, or similar.

Sometimes the term head of government is also used, which I think is usually the same as the leader of the country.

[joshuaissac]

In parliamentary republics, the president is the head of state (and has little actual power), while the prime minister is the head of government.