There is not much of a difference between the two determinatives.
In the singular, the main difference that exists between um and algum is the fact that algum doesn't admit a [+specific] reading (i.e., a reading where the speaker has a specific entity in mind):
Vou comer uma maçã: a Fuji.
*Vou comer alguma maçã: a Fuji.
(Another difference is that algum, but not um, can be put after the noun in certain contexts, like não vou comer maçã alguma/*uma.)
In the plural this difference all but disappears:
Vou comer umas maçãs: as três Fujis.
Vou comer algumas maçãs: as três Fujis.
Algumas works more like a quantifier: the difference is small, but with algumas you're more clearly referring to small amount of apples. Therefore, with only two items, algumas is more awkward (as in vou comer algumas maçãs: esta e aquela). And if you explicitly request a count, alguns is clearly the better option, perhaps the only possible one:
— Quantas maçãs comeste?
— Comi algumas. / — ?/* Comi umas.
An alternative is to respond with comi umas poucas (literally a few).