I have to admit, I've never been real clear on exactly how sentient droids are, a lot of them sure seem to act sentient, but they aren't treated like it. And some people almost seem confused or disgusted when they're treated like anything more than a walking computer.
I guess maybe it's like animals in the real world where some people just treat them like they are, and others don't give them that much consideration.
There's been a number of sources, like the
Essential Guide to Droids, which suggest that their range of intelligence and even potential sentience varies widely. A protocol droid like C-3PO has a much more complex intelligence as a means to facilitate his role, like his fluency in so many languages, whereas other droids like power droids (at least per the EG) are considerably less intelligent because they're mainly only meant to be mobile batteries. They have advanced diagnostic programming to make sure they don't accidentally charge an unstable power source, but beyond that they might walk off a cliff before they realize they should change direction.
Droids like astromechs seem to have a wide variety of potential, as technically they're supposed to undergo routine maintenance that would prevent any unusual "quirks" developing in their personalities, but many living beings prefer not to do that because they like having those quirks. R2-D2 would certainly be a good example.
There are other droids whose programming can be potentially vulnerable to hacks, like the droid bartender in the EG. It's a popular model for busy starports and other locales, but it's not uncommon for the droids to suffer mishaps if a clever slicer messes with their programming. Endless free drinks or, potentially worse, telling it to mix up drinks that are chemically incompatible (and usually explosive).
So I would personally say it's a variety, in terms of what different droids are capable of and how living beings respond to them.

It's not unlike how Data and the VOY EMH could be considered Trek examples of fully sentient artificial life, but not all artificial intelligence would necessarily be on their level.