Don't worry, neither do physicists. When people talk about 'quantum gravity' they mean some theory which unites curving of space with the idea of gravity being

Don't worry, neither do physicists. When people talk about 'quantum gravity' they mean some theory which unites curving of space with the idea of gravity being 'quantised' in particles. Only string theory does this consistently (and here the curvature manifests itself as a background of gravitons), but string theory isn't really a serious competitor for physics beyond the standard model.