If you have a specific NEMA-T frame motor, you can be assured that, regardless of manufacturer, that specific T frame (for example, a 324T) will have the same shaft length, shaft diameter, and bolt hole mounting dimensions. What too many people don't realize, however, is that the physical size of specific T frame motors can vary greatly. That means you could buy what you are assuming is a simple drop-in replacement that doesn't quite fit in the space allotted for it.
NEMA Class Designations
NEMA, which stands for National Electrical Manufacturers Association, revolutionized electric motor manufacturing by using a motors's starting-torque and accelerating load to categorize it into specific classes. NEMA standard motors make it much easier for you to find the right one for your particular application.
The four standard classes they developed are NEMA A, NEMA B, NEMA C, and NEMA D (and very large motors classified as Above-NEMA). Each classification has certain applications they are well-adapted for (e.g., NEMA C is for situations that require high starting torque while NEMA A motors lend themselves to applications that require a high speed at full load).