This is far from standard, but in my mind, when I'm doing algebraic geometry, "quasicompact" means "compact in the Zariski topology," and "compact" means "compact in the analytic topology" (or is not used at all if I'm not working over a topological field). Thus, in principle, having explained that the terms were being used this way, one could write statements like

"$\mathbb{A}^n_{\mathbb{C}}$ is quasicompact but not compact"
and
"Projective varieties are both compact and quasicompact."

But I would be very hesitant to do so, since I've never seen the terminology used this way so explicitly.