>I thought Alexander was just a conqueror basically, the same as any other empire like Rome

Rome, who famously didn't colonise anywhere? https://en.wikipedia.org/wiki/Colonia_(Roman) and https://en.wikipedia.org/wiki/Colonies_in_antiquity

Although people tend to talk about colonisation as being a modern process, it's arguably much older, and empires have been doing it as long as they have existed. It's what makes them empires.

>and I realized I am not sure of what exactly qualifies as 'colonization'.

You colonise a place when you assert control over it, and physically establish your 'superiority' in matters of law and culture, compelling the indigenous people to either remain subservient and/or convert to your ways. Rome is one of the best examples of this, constantly seeking a controlled influx of people via the foederati, establishing Roman citizenship as something to be sought after, etc.