- He is regularly buying food in the market.
- He regularly buys food in the market.
It seems they all refer to the same thing that 'he buys food in the market regularly'? what's the difference?
The simple present should be used for discrete actions that occur regularly, habitually, or repeatedly:
He regularly buys food from the market
He habitually takes a shower every morning
He repeatedly checks his phone whenever he is out of the house.
The present progressive is used for actions happening in the moment:
Look. He is checking his phone, again.
He isn't home -- he is out buying groceries from the market.
It's morning, so he is taking a shower.
However the present progressive can be used to indicate actions that happen so frequently it seems like they happen all the time. In this case the sentence should include an adverbs like always, continuously, constantly, nonstop, and so on.
He is constantly checking his phone when he's out of the house. It's so annoying!
He is always eating at restaurants instead of buying food from the market.
As with many things in language, the adverb-verb combination has to make sense. Since regularly means at regular intervals, combining it with the present progressive is confusing. It's a contradiction to say that something happens regularly then imply it happens all the time.
To be clear: it's grammatical, and possibly something people say without thinking too much about it, and the intention is clear. But it sounds like a poorly constructed sentence, or something a non-native speaker might say.
The second way, with the simple-present, would be the normal way to express this. The sentence expresses a fact about the person, that doesn't change.
The first sentence is slightly odd. It suggests that the regular event is temporary. It could emphasise a change to the market
Since the supermarket shut he is regularly buying food in the market.
Or maybe to emphasise the change to regularity:
He used to go shopping whenever He ran out of food. But since the baby came I need to be more organised. Now he is buying food in the market regularly.
As is usual, the present continuous can imply the changing or temporary nature of an action.