'Sommige' can be seen as a subset of 'alle' (all):
- 'Sommige herten eten' > 'some deers eat' (and some don't)
- 'Sommige boeken zijn groot' > 'some books are big' (and some are not)
'Wat' is used for more in the sense of an amount.
- 'Ik wil wat water' > 'I want some water'
- 'Ik koop wat meubelen' > 'I buy some furniture'
I don't think you can use 'sommige' with uncountable nouns (water, sugar, rice, power, rice). Maybe somebody can confirm that?
With countable nouns, there is a small difference:
- 'Ik zie sommige boeken' > 'I see some books' (implying that you're aware that you don't see all of them)
- 'Ik zie wat boeken' > 'I see some books' (without further implication)
Consider the English sentence "Some deer want some water". These are actually two different uses of the word "some". The first one means "not all", and the second one means "a bit of". In Dutch, two different words are used. The first one is translated using "sommige", the second one using "wat". Hence "Sommige herten willen wat water".