No, these terms do not refer to the same people. Palestinian national identity and peoplehood, while by no means as young as some like to argue (i.e. some who argue, using selective quotes, that it arose in the 1960s) does not date back to or necessarily identify with the Philistines. There are some in Palestinian society who identify as the descendants thereof, typically in politically charged situations, as well as claiming descent from Canaanites and the like, but they do not identify politically or in national terms as Philistines. I am no genetic expert, but studies have been published showing a common ancestor among Palestinians and Jews (including Ashkenazi, frequently described as "European", Jews) that does come from the Levant around those ancient periods.

As for whether this Philistine connection, the myth largely revolves around the similarity in the names, and ends there. There have been some portrayals, both positive and negative, of Palestinians as Philistines in Israeli and Arab society, to argue about native status or to argue about the political aspects of the conflict being religiously infused. I would not say that this is a major strand of argument necessarily for anyone, on any side of things, and certainly not historically validated at any rate. I also am not sure that "globally dominant opinion" has historically viewed Israel as the victim and Palestinians as aggressors; the history of portrayal of the conflict is complex, but the United Nations has in the past suggested that Israel's very existence is racist (in a General Assembly resolution that was passed in the 1970s and revoked in the 1990s). I will stay well within the 20 year rule and avoid commenting on anything later than that, but I do suggest that global opinion may be more complex than your initial question frames it.