Would "my stores are in the market" also be correct?
yes of course !
'di' means in, at, or on
the suggested translations sounds like your stores went to the market to buy something. it should be 'in the market'
I consider shops and stores as the same
It should actually be "in". "At" indicates a temporary position, rather than a permanent residence, and applies only to people at that. "I am at school" BUT "The bus is in the school" and "The janitor lives in the school".
Usually market stalls are temporary set ups : tent/umbrella, trestle table etc
"At," though commonly used in this context, is grammatically incorrect. "In" is the correct word.
'Stores' in Australia means separate shop buildings. Markets usually have 'stalls'.
"My shops are in the market"