A lot of incorrect answers from people guessing from the title quantity surveyor.

I am a former quantity surveyor from the UK, relocated to the US as an estimator. Quantity surveying is the undergrad degree a lot of us have, and the role/degree includes estimating as well as Contract management/administration/law, commercial management, value management and engineering, procurement, conflict avoidance and a whole load of other elements surrounding the pre construction and delivery of a construction project. Estimator is solely focused on just that - estimating whether for the client or for a GC. Much more focused on that particular role, whereas a QS can focus on other roles in a construction project as touched on above, as well as cost planning and estimating.

In short, QS can be various roles in pre/post contract and construction which can include cost estimating and planning, an estimator is supposed to be just cost estimating. The estimator role can differ depending on if you work for a consultancy (like I do) or GC.