There is a spectrum between the extremes of Covenant Theology and Dispensationalism, but in short they represent two sides of the continuity and discontinuity debate over the Old and New Testaments.
Dispensationalism says there is no substantial continuity between Israel in the Old Testament and the Church in the New Testament. In fact, even within the Old Testament and the New Testament there are multiple dispensations in which God interacts with humanity in very different ways. These dispensations can be unexpected: there are three dispensations in only the first 11 chapters of Genesis, but no dispensation focused on David and the Davidic Covenant. In this diagram from gracegospelpress.org each of the arrows represents a dispensation in which God's primary way of interacting with God's people was different:
The implications of Dispensationalism are seen most clearly in how they understand the promise/covenant of the Promised Land: the promise that the territory of Israel would belong to Abraham's descendants forever belongs to the people of Israel forever. While this promise was partially fulfilled during the time of the Monarchy, it is still waiting for its final fulfillment. So Dispensationalists usually anticipate that the biological nation of Israel (not necessarily the current country of Israel) will gain control of the entire land promised in Genesis 15, from the "Wadi of Egypt to the Euphrates". This is entirely separate from God's dealings with the Church. Many descendants of Abraham will also be part of the Church, but being part of the Church doesn't mean you'll be part of Israel. This focus on the fulfilment of Abraham's covenant as he would've understood it (and not just spiritualised away into the idea of inheriting the Kingdom of Heaven) leads most Dispensationalists to focus on an earthly eschatology, a pre-millennial return of Christ and a 1000 year reign of Christ in the current Middle East.
Covenant Theology represents the extreme in the other direction, that we should not see any real discontinuity between Old and New. You might expect from the name that Covenant Theology would be focusing on the Biblical covenants of Noah, Abraham, Mosaic, David, and New, but that's not actually the case. Instead Covenant Theology refers to the three "theological" covenants: the Covenant of Works, that God would give life to humanity as long as they remained righteous, the Covenant of Grace, in which God would save his people, and the Covenant of Redemption, which is a covenant between the persons of the Trinity, in which the Father appointed the Son to be the one to become incarnate and die for the atonement of God's people. The Biblical covenants are considered administrations of the singular Covenant of Grace, which means that each of the Biblical covenants has the same purpose, the same covenant parties, and the same benefits, so that the differences between the Biblical covenants are considered to only be incidental. It is because the covenant parties are considered to be one, the People of God, that Israel and the Church are considered to be One people, or why people say that the Church is the New Israel.
Because there is ultimately only one covenant between God and his people, and because there is only one people of God, Covenant Theology does not anticipate a earthly fulfilment of God's promise of the land of the levant. In this era of the church, the promise of the land is seen as being taken up inside the larger promise of the spiritual Kingdom of God; in the future it will be expanded again into the New Heavens and New Earth. But even if there would be in some sense a land of Israel in the New Earth, the promise wouldn't have any particular connection to that land. In the administration of the Abrahamic Covenant the promise of the land of God was seen as referring to the land that Abraham walked, but in subsequent administrations the same promise is now seen as referring to a larger land. In essence, the eternal promise was not to a particular piece of real estate, but instead that God would provide a home for his people. That real estate can change, but the promise to provide it does not.
So no, it's definitely not just a matter of terminology. Dispensationalism doesn't focus on the covenants - only four out of the conventional seven dispensations align with a Biblical covenant, and there is no distinct dispensation for one very important Biblical covenant, the Davidic Covenant. And on the other hand, Covenant Theology does not actually refer to the Biblical covenants, but the "theological" covenants of Works, Grace, and Redemption.
To return to the beginning, Covenant Theology and Dispensationalism represent the extremes of continuity and discontinuity, but they are not the only frameworks Protestants have for understanding how the Old and New Testaments work together. In particular, Reformed Baptists in the US have been doing a lot of good work in recent decades to find some middle paths between continuity and discontinuity. In my opinion their frameworks give a more appropriate emphasis to the Biblical covenants than either Covenant Theology or Dispensationalism do, and I think it's likely their popularity will grow globally in the future. Look out for names like Beale, Gentry, Wellum, and Zaspel.
