Gage R&R is applied to the measurement system as a whole - parts, instrument, operators, environmental conditions etc etc... Gagr R&R tries to isolate the contribution of variation due to Appraiser (AV), that due to Equipment (EV) and the actual variation in the parts(PV). Total Variation(TV) has all these three components. The aim to ascertain if the instrument is suitable to measure the part/characteristic in question. It is many times called the gage capability study and the R&R is the Measurement Error.
From instrument calibration point of view, the measurement errors are classified as either Random & Systematic errors or Type A /Type B errors, the result is measurement uncertainty......I think I better leave this one for the experts on the forum.
-Atul.