Hello,
I’m going to do some clothes shopping.
I’m going to go shopping for clothes.
I googled “do some clothes shopping” and there are over 72,000 results. What’s the difference between the first sentence and the second one? I guess the first one seems more casual than the latter, but I’m not sure. What do you think?
Thank you in advance,
sweetpumpkin
I don’t really think of one being more casual than the other. The second sentence is more common in AmE.
The structure changes if you change ‘clothes’ to ‘groceries’.
I’m going grocery shopping.
I’m going to the grocery.
“I’m going shopping” without specifying where, is used by some people for grocery shopping. Personally I find that confusing.
Thank you very much for your attention, NearlyNapping. So you mean the two sentences have the same meaning, right? In school we learn the second one (go shopping), so I found the first one (do shopping) interesting. 
Yes, they mean the same thing.
You can not say ‘do shopping’. You need the word ‘some’ or another quantity.
I’m going to do some shopping.
I’m going to do a lot of shopping.
I’m going to do a little shopping.
Nor can you use ‘go’ with a quantity.
I’m going to go some shopping.
I’m going to go a lot of shopping.
I’m going to go a little shopping.
Another version would be:
“I’m going to do the shopping”
In this case, the listener knows what shopping needs to be done, such as weekly grocery shopping.
However,
“I’m going shopping.”
Or
“I’m going to go shopping.”
Are both more common.
To me, it may also imply as follows.
I am going to do some shopping. (You have only a faint idea about what you may buy or, in other words, you have not decided on the items you want to buy)
I am going (going to go) shopping. (You have a clear idea about what you want to buy or, in other words, you have decided on the items you need to buy)