What really means stochastic in field of signal processing
Well, getting a bit linguistic, according to the Oxford dictionary:


  stochastic (adj.): Having a random probability distribution or pattern that may be analysed statistically but may not be predicted precisely.


So the definition would be the first one (I don't know where you might have found the second one as you didn't put any source about it). Nevertheless, regarding your specific question, SGD is indeed stochastic. It is an iterative method, but this doesn't mean it is not stochastic. It is iterative and stochastic at the same time: the two concepts are not related to each other.

To put it clearer: if something is blue, couldn't it be big? Well... why not? That's exactly what you are asking here. As size isn't related to colour (absurd example that I think can help here), an approximation can be iterative and stochastic (such as SGD): being one thing doesn't mean it can't be the another one too.