Gaza is not a country, it is part of a country in the Middle East called Palestine.
The Gaza Strip, most commonly referred to as just 'Gaza' is a region in the country of Palestine. It is known as an exclave region, which means it is entirely surrounded by the territory of another state (Israel).
It is on the east coast of the Mediterranean sea and borders Egypt on the southwest.
When people talk about Gaza, they are referring to this small region in Palestine, which has recently been subject to much war and turmoil due to differences with the Israeli state over land and autonomy. The current eminence of the situation in Gaza, and the dispute over who owns how much land (between the Israelis and Palestinians) may be why this region in general has been subject to some confusion.
I hope this answers your question.