My father (87 y.o.) has a lot of trouble hearing and has been through several sets of hearing aids.
The low-end models are basically just amplifiers. The higher-end models are definitely adjusted to specific frequency ranges (per audiologist evaluation).
Oddly, my father dislikes the high-end ones and insists on using the cheapo ones he got via Internet. OTOH, he dislikes wearing hearing aids in general, and often goes without or uses just one of a pair. But he's also developed Alzheimer's-related dementia, so it's difficult to reason with him.