How to classify power electronics components in 2 main groups?
It depends why you want to break them into groups.

If you simply want to partition the course into more easily managed teaching sections, then an alphabetic grouping is just as rational. Put all the power devices into alphabetic order, and split them into two.

If you want to group them by the way they're used, then the groups you've chosen aren't too bad. The second group covers quite a range of technologies, and the first controlled and uncontrolled behaviours, but if you want to reduce the number of groups, that's what you end up with.

If you want to group things with similar underlying physics, then your groups are not suitable. For instance, the progression one junction diode, two junction BJT, three junction SCR is quite natural. The different method of operation between a BJT and a FET is very significant.

If you want groups that are meaningful on both behaviour and underlying technology, then you're going to need a bigger set.