Short answer: `BT40-ER32` is a BT40 machine-taper holder fitted with an ER32 collet chuck; it holds tools from 1 mm to 20 mm shank diameter. The BT40 end goes into the spindle (7:24 taper, JIS B 6339, pull stud M16), the ER32 end grips the tool.
Collet range is set by DIN 6499. A 12 mm end mill needs ER32 or larger; an ER32 will not close on a shank outside 1–20 mm.