A simple comparison between As vs When

CED, under as, when and while, has

from English Grammar Today

As, when and while are conjunctions. In some uses as, when and while can mean the same, but they can also have slightly different meanings. We use them to introduce subordinate clauses.

though this isn't a full explanation (although I'd argue that subject/verb deletion from an original like 'when we were kids,' ... to 'when kids,' ... licenses the 'conjunction' label here).

On the other hand, ODO looks at the surface structure here:

as preposition ...

2 During the time of being (the thing specified)

‘he had often been ill as a child’

In 'As managing director, I have to make tough decisions', 'as' means 'in my role / capacity as' or 'Because I am'. This usage undoubtedly adds at least a nuance to the meaning of 'as' in 'As kids we didn't complain about being poor', but I'd say that the purely temporal 'When we were kids ...' is a closer paraphrase.