CAT, BT and HSK are the three common spindle tapers that decide which toolholders fit a machining center. They are not interchangeable, and the right one depends on where the machine was built and how fast and hard it cuts.
CAT (V-Flange)
The North American standard, a 7/24 steep taper with a V-flange and a pull stud. CAT40 is the general-purpose size; CAT50 handles heavy cutting. Rugged and everywhere in the US.
BT
The metric equivalent, common in Asia and Europe. Same 7/24 taper angle as CAT but a symmetric, metric flange and pull stud — often considered better balanced at speed. BT30/40/50. Not cross-compatible with CAT despite the matching taper.
HSK
A hollow, short taper that contacts the spindle on both the taper AND the face (dual contact) for maximum rigidity and repeatability at high RPM. The choice for high-speed and 5-axis work. Sized by flange diameter — HSK-A63, A100.
Bottom line
Rule of thumb: CAT for general US shops, BT for metric/import machines, HSK when you need high spindle speeds or 5-axis rigidity. The number (40/50/63) is the size — bigger means heavier-duty. Holders must match both type and size.