Personally I would include in the vacation budget almost all expenses that are incurred while on vacation. One reason is that I usually eat out a lot more when on vacation than I do when at home, so my normal dining-out budget would not be a realistic estimate of how much I'd spend dining out on vacation. Also, in terms of planning expenses, it's easier to do calculations like "to go on this trip I need to save $5000" or whatever if the budget is "all-inclusive".
You mention "shopping" as a category, but from my perspective that is too general to be a useful category. Shopping for what? Most of the "shopping" that I do while at home is for fairly ordinary things (groceries, tools, cleaning supplies, etc.), and I don't do much shopping of that sort while on vacation. Conversely, if I do shop for things like souvenirs or gifts while on vacation I'd generally categorize that as part of the vacation spending.
If I go on vacation and just happen to find something I wanted to buy anyway, I'd probably track it under its normal category. For instance, if I had been looking for a leather jacket and found a nice one while traveling I'd probably track that under "Clothing". I do this fairly often for things like books, but the amount of spending in these categories is fairly low overall, and even lower on vacation, so it's not super important to track them with exact accuracy. But general "entertainment" while on vacation (e.g., admission fees to museums or tourist attractions) is categorized as "vacation" spending.
It's also worth noting that some budgeting/financial software will let you create subcategories. I use Quicken, where I have a category "Vacation" with subcategories "Vacation:Travel", "Vacation:Food", and "Vacation:Lodging". I find that in practice these three subcategories account for the vast majority of vacation expenses.