What are the differences between malts used to make

1. Scotch
2. Beer
3. Malted Milk Shakes

It is my experience that the malt syrup that is sold for making beer is unsuitable for making malted milk shakes and flavoring for malted milk shakes is damn more expensive. Also, I remember that about 60 years ago there was a solid, brown, otherwise transparent, strongly flavored malt candy that came in broken chunks and tasted the same as the flavoring used in malted milk shakes. It doesn't seem to be available anymore.

It also seems to me that various Scotches taste more or less close to either beer or the flavoring used to make malted milk shakes. Does anyone have any insight into this?