These two verb expressions are often confused by non-native English speakers. Let’s look at the differences.
Both of the expressions involve the idea of buying something. So, what’s the difference?
To go shopping means that your intentions are to buy things because you want to or because you need a new version of something. There isn’t necessarily any routine aspect to this action.
example: I like to go shopping the weekend after payday. I need to go shopping for a new coat.
To do the shopping describes the regular process of going to the supermarket to buy food and the other necessary items we need to live on a day to day basis. There is an aspect of doing this regularly and it is more of an obligation than an enjoyable activity, for most.
example: My wife always does the shopping, and I do the cooking.
Does that help? Don’t forget to mentally practice these words.