All right, let's get some terms straightened out here.

The land of Canaan is basically just an ancient geographical term for what most scholars refer to as the Southern Levant (modern-day Lebanon, Israel, Palestine, the western part of Jordan and southwestern Syria). The name is found in the Hebrew scriptures and also in the Amarna letters, which are a series of correspondences from Canaanite vassal kings to their tributary lord in Egypt about various political issues. It's a geographic term for the area. The people who lived in this area prior to the Iron Age are what we call the Canaanites, and their society was based around city-states, where one powerful city would rule a "hinterland" around it, and the area of these was not particularly large, as we have examples of city-states centered around Jerusalem, Gath, Ashkelon, Gezer, Shechem, Lachish, Hazor, and others. If you look at these on a map, you can see they are fairly close together. This book discusses the development of the Canaanite city-states.

Now that we know what Canaan is, what about Phoenicians? For that, we have to touch on the history of ancient Israel. The Israelites appeared at the end of the Late Bronze Age, and took over most of the Southern Levant, in the area of modern-day Israel. The exact nature of this is somewhat debated, as scholars such as Israel Finkelstein suggest they are just another group of Canaanites who rise up and take over, while others maintain some group of people moved in from somewhere else and took over. Whatever happened, the easternmost city-states fell first, and the new people moved west (this can be seen in the texts of the Amarna letters, with Shechem and Jerusalem falling first, and then the rest). This new people group became known as the Israelites, and they eventually set up two kingdoms, Israel and Judah, which are both historically attested by extrabiblical texts including the Mesha Stele and the Tel Dan Stele. The original inhabitants of the land were either absorbed into this new ethnic group known as the Israelites, or pushed northwest into modern Lebanon, where they founded the kingdoms of Tyre and Sidon and became what we think of as Phoenicians. They could not go south, because the Sea Peoples had settled the Levantine coast in the area now called the Gaza Strip (plus a bit north), and the central area was occupied by the Israelites. So the Phoenicians were the remnants of the Canaanites after they were displaced by the Israelites.

Now that we have that sorted out, let's talk about international relations. We know that relations between the two groups was quite friendly. Hiram King of Tyre is recorded in 1 Kings as supporting the reign of David and Solomon, and trading with Solomon for many of the goods used to build Solomon's Temple, even providing building experts. Further down the line, we see the Israelite King Ahab married to a Phoenician princess (Jezebel) in 1 Kings 16-20. Throughout the Scripture, which we regard as Israel and Judah's records from these periods (at least the "historical" books of Kings and Chronicles), we see them in alliances and as trade partners. I cannot think of a single war or military conflict between the two. Israel and Judah had plenty of wars with Aram (based in modern Syria), but none with Tyre or Sidon.

Therefore, during the classic Phoenican period, the Phoenicians may have thought of themselves as Canaanite, as they are the descendants of a Canaanite city-state, and probably saw the Israelites as another friendly nation. Both had different religions.

Does this answer your question?