M2 is the taper inside the spindle.
J2 is the taper inside the drill chuck.
The drill chuck is held by friction on the small angle J2 taper. To assemble it make sure everything is really clean and dry, insert the taper in the chcuk and give it a good bang with a brass hammer or something softer than steel. It need never come off.
The M2 taper is held in the machine by tightening the drawbar but not too tight, as you now know.
To hold milling cutters you need a set of M2 collets which are a standard item probably from the same place you got your mill.
An open mind is a virtue...so long as all the common sense has not leaked out.