> ... the UK perspective.
Drogerie: chemist (e.g. Boots, Superdrug, DM, Rossmann)
Apotheker: pharmacy (Knights, Lloyds, Adler)
It's not that clear-cut in the UK either. There's much more overlap in the use of the term chemist/chemist's.
A chemist/chemist's/chemist's shop usually has part for selling health and beauty products/toiletries/OTC medicines plus a pharmacy section where medicines are dispensed.
Boots (formerly Boots the Chemist) nearly always has a pharmacy section with a dispensing chemist/pharmacist. Superdrug stores are mainly health and beauty retail stores that may sometimes have a pharmacy section. (I don't think we have Rossmann's in the UK so I can't comment).
Some chemist's use "pharmacy" as part of their name (Lloyds, Knights, Rowlands), but even when I go to the Rowlands Pharmacy nearby, I would still say that I'm going to the chemist's.
Supermarkets have shelves for over-the-counter medicines (general sale list (GSL) medicines that can be sold in general retail outlets without the supervision of a pharmacist) and they may -- but mostly don't -- have a pharmacy section for dispensing prescription only medicines (POM) and pharmacy medicines (P)that may be sold in a pharmacy without prescription, under the supervision of a pharmacist (which explains why you can't find them on the shelves for yourself, even tho' you don't need a prescription).
Drogerie: health and beauty (retail) store/chemist's e.g. Boots, Superdrug
Apotheke: dispensing chemist/chemist's/pharmacy e.g. Boots, Knights, Lloyds, Rowlands
BTW Apotheker is the pharmacist and not the pharmacy.
If you really need to emphasise the difference, how about (for BE):
"People are happy that they can buy the product in a high-street/budget health and beauty retail store rather than at an expensive chemist's/pharmacy."