Overspeed is the major concern regarding rotating parts. Exceeding redline by specific amounts can get you into trouble with part resonances and major failure conditions where blades come unfixed.
Overboost can get you into trouble by altering the cycle to the point where non-controlling temperatures (like in the aft parts of the compressor as well as the forward stages of the turbine) cause internal damage which must be assessed in a forced maintenance action.
Regardless of possible confusions between what different manufacturers use in their wordings, just follow the manual for the product.