A common theme in geometric group theory is to try to understand when two groups are quasi-isometric (or "geometrically close") and when they are commensurable (or "algebraically close"), and when these two notions coincide. Davis-Januszkiewicz showed that every right-angled Artin group (RAAG) is commensurable to some right-angled Coxeter group (RACG). It is not hard to see that the reverse is far from true, prompting the question: Which RACGs are commensurable to RAAGs? I will talk about joint work with Ivan Levcovitz which explores this. In particular, we show that for a large class of RACGs, being commensurable and being quasi-isometric to a RAAG are equivalent. The talk will be aimed at a broad audience.