I used to be very slim but stocky. Now I'm fat but still stocky.
Stocky means broad shoulders. Solid midsection with a well developed musculature but lacking in height. Fat is something else entirely.
Well that's like saying the traffic light was pink, when you run a red light. Similar but not the same.
These days, if a guy isn't built like a brick spithouse or rail thin, many folks would say he's fat. Body dysmorphia - it's not just for women anymore!
Stocky is just solidly built .. maybe a little chubby .. but not fat or flabby.