I use the terms primarily to describe ethnicity, but sometimes also cultural identity which crosses countries. I do that when it seems the accurate term. I can't guarantee that I haven't mistakenly used it in other ways, but accuracy is generally my intention.
I use the term 'Arabs' when the discussion requires me to distinguish people of the ethnicity who originated on the Arabic Peninsula - who tend to share a culture - from people of Jewish ethnicity - who tend to share a different culture.
I especially use it when talking historically about a time when both lived in the area which now forms Israel, and the people of Arabic ethicity didn't have any other specific national or cultural name to identify them.
I find it revisionist to use the term 'Palestinians' for Palestinian Arabs when talking about the period before 'Palestinian' became a national identity in the 60s.
The British did talk about 'Palestinian Arabs' and 'Palestinian Jews' - but at that time 'Palestinian' referred to the region rather than a specific national identity - in the same way as we might refer to 'European Jews'. I drop 'Palestinian' from both when it's obvious we're talking about that region.
I also use it for current people when I'm talking about a cultural identity across a number of nationalities, very much as I'd use the term 'Europeans' to group British, French, German, Italian people when talking about some shared cultural ideas. 'European' describes a geographic area, but it can also be used to describe shared traditional culture across the different countries, where that shared culture stems from our shared history, from a time when people didn't tend to travel so far. (Of course, we also sometimes use the term European to describe citizenship or geography)
I don't think either term is offensive when used in that way.