The two peoples are actually separate groups.

The Philistines lived in the Coastal Plain region of modern Israel (the area including the Gaza Strip and up past Tel Aviv), with their main cities including Ashkelon, Ashdod, Gaza, Ekron and Gath, and the Phoenicians were concentrated north of modern Israel in the area of modern Lebanon, and their main cities were Tyre and Sidon.

The Philistines were one of the Sea Peoples, a number of invading raiders from the general northeastern Mediterranean. The peleset as they were called (which is where the name "Philistine" comes from) originated somewhere in the Aegean, perhaps near the Greek islands close to Turkey. We have not yet been able to pinpoint the exact homeland of the Philistines, but we know it is the Aegean world because of what we have found archaeologically in the earliest Philistine sites in Israel. The most telling feature is their pottery. The earliest Philistine pottery is in a style called "Mycenean IIIc", which is a direct parallel to the style of pottery found in the Greek city of Mycenae in the Late Bronze Age/early Iron Age. Other Aegean features that have been observed include architectural features such as square hearths. We know they were part of the Sea Peoples because they are mentioned in several texts describing the groups that made up the Sea Peoples, such as the most famous depiction of the Sea Peoples, the Medinet Habu reliefs, which describes the invasion of an alliance of 7 Sea Peoples (the Denyen, Peleset, Shekelesh, Sherden, Teresh, Tjekker, Weshesh) and their defeat at the hands of the Egyptian Army. The Peleset are, we understand, the Philistines.

The Phoenicians, on the other hand, are descended from the original Canaanite inhabitants of the land. As other groups moved in, (such as the Israelites and the Philistines) the Canaanites were relegated to the edges, and the ones living in modern-day Lebanon were forced to look to the sea for economic survival. The way the geography of the region works, the mountain ranges mean that there is not as much fertile land, and therefore civilization is forced toward the coast, and encouraged the Phoenicians to look to the sea and mercantile trading to succeed economically, and they became one of the most powerful economic forces in the Mediterranean, establishing colonies all the way around the Mediterranean, as far away as Spain. In fact, the famous city of Carthage (you know, the place Hannibal was from, who famously crossed the Alps to attack Rome with all the elephants?) began as a Phoenician colony.

Probably the reason you confuse the two is because they are both supposed to be seafaring peoples. In actuality, the Phoenicians were the ones who really made their bones on the sea, while the Philistines did trade, but primarily stayed at home, and developed a lot of agricultural products, being situated on the fertile Coastal Plain.

Does this answer your question?

Let me know if you have any more questions, and I would be happy to clarify or answer them!