Having a high social status may not bring happiness by itself but it certainly won't hurt.

When I was in early grade school, I was unpopular and a target for being picked on. I was unhappy about that and launched an in retrospect quite cynical campaign to increase my status. Basically, I targeted the highest-status boy in my class and devotedly worked to become his friend. I invited him to events and talked with him and laughed at his jokes. I didn't particularly like him, but I was successful and took up a role of second-highest status boy. Then I ruthlessly defended my position.

Second grade was kind of weird.

Anyhow, I have to say that as weird as I see it in retrospect, it worked pretty well for me. I didn't super enjoy maintaining my relationship with the other boy, but I liked it a lot more than being a low status person others picked on.

I make no grand claims to universality.

They're different concepts, obviously (hence the different names for them), but they correlate strongly.