Shifter is something that technically anyone could come into. It's not necessarily inherited, though the temperament required may be influenced by inherited traits or upbringing. Most people won't be able to become a shifter, though. The primary trait of the Shifter is that their sense of self is mostly unaffected by their physical form. While most people develop a sense of identity that includes their body (eye color, hair color, race, gender, clan, etc), the shifter's identity is mostly internal. And that internal identity becomes more and more internal and less and less based on physical form as they go down that path. Their sense of self is so independent of their physical form that they are able to slip into other forms without any mental or emotional hangups. They change shapes like someone else might change weapons.
It is this sense of self that makes generalizations about shifters hard to make. Every shifter is going to be unique. I've seen many stereotypes talked about concerning shifters, like the assumption that they use their shapes as a form of camouflage. Like the only reason a shifter might be a deer is they don't want to be known as a shifter so they can spy on people. Many shifters may do this. Some may even have that as a main motivation for being a deer. But others may just find being a deer at the moment to be the most fun or pleasant or whatever. It might have nothing to do with stealth or espionage. There aren't really any rules to being a shifter, other than the mentioned sense of self being so strong as to not being defined by external factors.
NWN made Shifters an extension of the Druid, but in PnP this isn't a requirement. Wild Shape is just one of several means to become a shifter. Amia doesn't require a druid background, though it does still require the Druid levels OOCly at least. If you aren't a druidic shifter, basically you just ignore the druid levels and don't use the spells and abilities granted by them. My shifter is a druidic one, and I'm not really sure what nondruid shifters tend to have as their shifter basis.
EDIT: I forgot about this (player-made, I think) Shifter FAQ:
viewtopic.php?f=2&t=44671