There is some overlap, but they are not quite the same.

The people we call Phoenicians were the Canaanite inhabitants of certain coastal city-states in the northern Levant, particularly Tyre, Sidon, Byblos, and Arwad. Tyre, Sidon, and Byblos are located in what is now Lebanon, and Arwad is located in what is now Syria. Note that "Phoenicia" and "Phoenician" are Greek exonyms, and there is little evidence for a collective sense of identity among the inhabitants of these cities.

The Phoenicians who lived in some of the coastal cities in Syria (and Lebanon) were not the only inhabitants of ancient Syria. In the Bronze Age, their neighbors included powerful kingdoms like Yamḫad (an Amorite kingdom based at Aleppo) and Ugarit, a coastal city in what is now Syria that functioned as the main hub of trade in the northern Levant. In the Iron Age, Phoenician cities competed with the (Neo-)Hittite and Aramaean kingdoms of southern Turkey and northern Syria, such as Gurgum (Kahramanmaraş region), Carchemish (centered at modern Jerablus on the Turkish-Syrian border), Patin (centered at Tell Tayinat near Antakya), and Hamath (centered at modern Homs). These kingdoms engaged in trade not only with the southern Levant but also the Aegean and maintained port cities of their own, although the locations of these ports changed over time as rivers shifted and harbors silted up. For example, in the Hatay province of southern Turkey, Alalakh and its port of Sabuniye (Middle/Late Bronze Age) were replaced by Tell Tayinat and its port of Al Mina (Iron Age), which were replaced by Antioch and its port of Seleucia Pieria (Hellenistic period), which were in turn built over by Antakya and Samandağ.

For further reading, see Ancient Syria: A Three Thousand Year History by Trevor Bryce and The History and Archaeology of Phoenicia by Hélène Sader.

Also take a look at u/kookingpot's answer to What sort of relationship did the Israelites and Jews have with the Phoenicians?