Yes that's a good way of putting it. What I've seen around is talk that "measurement of one particle effects the other" and often people use the term "collapse

Yes that's a good way of putting it. What I've seen around is talk that "measurement of one particle effects the other" and often people use the term "collapse the wave function of the other particle" to articulate this (because they'd heard the term). The fact that the entangled state of the 2 particles is described by the same wave function resolves this.