We consider binary quadratic programs (QP) having a quadratic objective function, linear constraints, and binary variables. Many classical solution methods of these problems are based on exact reformulation of QP into an equivalent mixed integer linear program. Several linearization methods were studied in the literature. More recent solution methods also build an exact reformulation but into a problem which objective function is quadratic and convex. A common point of the two approaches is that the continuous relaxation of the reformulated problem is a convex optimization problem that can be solved in polynomial time. This makes it possible to use a general branch-and-bound framework to solve the reformulated problem and even to rely on the strongness of standard solvers. In this paper, we show that several quadratic convex reformulation methods, as well as classical linearization, can be viewed within a unified framework. This shows the non-surprising result that linearization is a particular quadratic convex reformulation on the one hand. On the other hand, it allows to compare these methods from a theoretical point of view.