Macgrumpy was mostly correct on his definitions of accuracy and precision but erred in his final interpretation of what exactly companies are guaranteeing. Accuracy and Precision are very often conflated, but have concrete scientific definitions.
Accuracy: Describes the closeness of measurements of a quantity to the quantities true value (e.g. in shooting, the average closeness of all your shots to the aiming point.)
Precision: The degree to which several measurements of the same quantity provide values close to each other. (e.g. in shooting how close the shots in a group are to each other, regardless of proximity to the bullseye)
If accuracy is measured by the distance between a bullet's impact point to where the sights were aimed. then a rifle shooting a 10-shot group measuring 1 inch diameter centered in the middle of the target at the aiming point is more accurate than another rifle shooting a 10-shot group measuring 1/4 inch that's two inches below the aiming point. Right?
Exactly, technically the rifle shooting the 1" group is more accurate, while the rifle shooting the 1/4" group is more precise.
Here is one of the many illustrations of accuracy vs precision online (not mine):
When rifle manufacturers give an "Accuracy Guarantee" they are actually giving a mechanical precision guarantee, only if they called it what it really is, most people would not know what they are talking about. They are telling you that with a certain ammunition their rifle is mechanically capable of placing 3 or 5 shots within a certain angular projection. It would be impossible for rifle manufacturers to actually guarantee accuracy, as that would involve regulating many variables that are not within their control. They can however tell you that their rifle is capable of a certain level of precision, which is why accuracy guarantees arent a gimmick, but they also arent really accuracy guarantees.