NOUN PHRASE, Biological problem and Biology problem

It is usual to use the adjective when available as a premodifier, rather than the attributive noun alternative, unless there are other factors in play.

There are many examples of the noun phrase 'biological problem' to be found on the internet. The adjective specifies the domain: compare 'societal problem', 'political problem'. A problem associated with / encountered when investigating biology (whether something where the solution would be quite useful or for the time being just good to know, or something needing an urgent solution, say a vaccine against Covid).

There are examples where 'biology problem' is used as a synonym (there's no law against this!), for instance:

• A computer just solved this 100-year-old biology problem.

[Popular Mechanics]

(though even here, 'problem' has a strong flavour of 'poser'; one thinks of Fermat's Last Theorem and chess problems).

However, 'biology problem' connotes quite strongly the classroom or other educational institution ("Have you managed to solve the maths problem old Tweedy set us on Monday?") and although the domain is still totally clear, more context is strongly hinted at. 'The problems we get in maths, physics, and biology.' More of an intellectual exercise flavour.

A "biological problem" is cancer, diabetes, invasive species, habitat loss, et al.

A "biology problem" is the argument between Darwinists and Creationists, etc.