The modal editing system
Understanding Blender's modal editing system before looking at the shortcut table will make it much less confusing:
G — Grab/Move. Pressing G enters grab mode. The selection moves with your mouse. Press X, Y, or Z to constrain movement to that axis. Press a number to move by an exact distance. Left-click or Enter to confirm. Right-click or Escape to cancel.
R — Rotate. Same modal pattern. Press R, then optionally an axis (X/Y/Z) and a number for exact rotation. Confirm or cancel.
S — Scale. Same modal pattern. Press S, then optionally an axis and a number for exact scaling.
This system applies in both Object mode (transforming whole objects) and Edit mode (transforming vertices, edges, or faces).