What really means stochastic in field of signal processing

I met two definitions of word stochastic, the first one (cited from wikipedia Stochastic)

The word stochastic is an adjective in English that describes something that was randomly determined

The explanation of stochastic and deterministic what is used in textbooks really make sense according to definition above. The second definition is

Stochastic means sample by sample

For example SGD - stochastic gradient descent.

This seems to be a little confusing for me. I do not really see any relation between random and step by step.

Do I miss something? Or it is really different meanings for the same word?

• 'Stochastic' never means 'sample by sample'. – Matt L. Feb 21 '17 at 16:40