I shouldn't pose as a dairy expert, but will share a few things I have
learned.

The word "casein" has the same root as "cheese" and was coined to
describe the proteins in cheese.  In the presence of calcium and
magnesium, casein is quite insoluble in water.  It can be dissolved by
overwhelming the calcium with sodium hydroxide, to form sodium
caseinate, which is somewhat water soluble and forms a very viscous
solution - or perhaps more of a water dispersion.

Lactose is a sugar, water soluble, which can be split into two other
sugars called galactose and glucose.  I am not aware of research into
whether it's the lactose per se or the galactose formed from it that
causes problems for lactose intolerant individuals.  Maybe that's a
source of some of the baffling contradictions that seem to haunt the
subject of LI.

Whey is the liquid drained from cheese curds after they are formed.
Whey is mostly water and contains the dissolved lactose as well as some
relatively soluble proteins.  If it were possible to completely remove
and rinse all the whey from the cheese curds, they should be quite free
of lactose.  Of course, this doesn't quite happen.  Apparently, aging
converts some of the remaining lactose.  (To galactose or what???).

The bottom line is, casein may contain a low level of lactose, depending
on degree of purification.  Highly purified sodium caseinate will have
very low levels, less than 1%.

Whey is extremely cheap because it is an unwanted byproduct of
cheesemaking and used to be a major water pollutant in dairy areas.
That is why whey powder is used in so many food formulations.  Whey
proteins can also be separated to some extent from the lactose.  The
early "whey protein concentrates" had more lactose than protein.  They
are somewhat purer now.

Don Maxwell