Exactly! Your distinction between these two theories is spot-on.

Even further, Mills' "racial contract" is, in fact, precisely that: a written contract drawn up and actually codified into law by white "elites", including but not limited to the constitution itself for example, and various pre-Revolutionary War (colonial) statues, ordinances and rules regulating "inter-racial" interactions from even before the beginning of this nation-state right straight through and beyond Slave Codes, Black Codes and Jim Crow laws.

Alexander's "racial bribe," as you note, is just that: a bribe to entice those non-elite whites to support "whiteness" as a tangible thing (see Chery I. Harris Harvard Law Review piece entitled "Whiteness as Property). The "racial bribe" is also in line with W.E.B. Dubois' notion of "the wages of whiteness" where he posits that many (if not most) white people can and do accept their lower actual wages and "lifestyle" in exchange for a "psychological wage": The assurance that they may be poor, but at least they are not BLACK.

As you so well point out, the end result of all of this, of course, is that a tiny minority of "elite" white people get to exploit both groups -- poor blacks AND poor whites.