  We prove that the set of Bowditch representations (introduced by Bowditch in
1998, then generalized by Tan, Wong and Zhang in 2008) and the set of
primitive-stable representations (introduced by Minsky in 2013) of the free
group of rank two in the isometry group of a Gromov-hyperbolic space are equal.
The case of $\mathrm{PSL}(2,\mathbb{C})$-representations has already been
proved by Series and independently by Lee and Xu. Our poof in this context is
independent.
