"White privilege" This ought to be obvious, but seldom is. Actually, that addition of "I reject for the most part" is crucial. Because to say differences between groups people don't exist at all, or are only the invention of the mind of some people, isn't right either. — ssu
Is it? My identity is defined by my relation to the world. That includes other people. There's family, neighbourhood, city, state, the world. I "borrow" from it all. Then there's how I relate to human history; get from my parents, studied in a university over 400 years old, live in a house I didn't build. Or as the ancient celts said: I draw water from wells I didn't build. There's nothing "individual" about my identity at all. It's one of the more persistent illusions of our time that the individualism is something to aspire to while it really is a degradation of society.
That's not to say we should blindly accept the position and relations that we are thrown in. In the end freedom is about accepting the chains we want to bind ourselves with; family, friends, kids etc.
So getting that back to privilege, I think the main differences can be found there: it's mostly about opportunity to be able to choose. Money makes it easier to choose, so people with more are privileged. Sometimes that's even unfair, e.g. inheritance inequality or exorbitant salaries or taxation rules disproportionally benefitting RoI over wages.
And there's definitely a privilege to being part of the dominant sub-culture within a nation and that's still being male, white, straight, no tattoos etc. All else being equal, I'm more likely to land a job interview than the guy with the foreign sounding name on his resume. All else being equal, I'm less likely to be stopped by police. All else being equal, people are less likely to call the cops when I'm tresspassing. Here's a nice video demonstrating that in the Netherlands, where being white makes all the difference: