Speaking in terms of US tax law:
While this is true, the organizational form a business takes (ie: sole-proprietorship, corporation, etc) does not impact the categorization of expenses. But rather (in some cases) how / where those expenses are reported.
1 monthly web hosting
2 monthly invoicing software web app (freshbooks)
There are no official, pre-defined categories for these expenses. A category such as "Service Fees" would do. This would then be reported in the "Other Expenses" section of the tax return.
3 photoshop magazine subscriptions
"Dues & Publications" is the common category used for this type of expense
4 scripts that i buy
This depends on your purpose for buying the scripts.
If these are scripts purchased for use in your own business, then they must be treated as capital assets, and "depreciated" over a number of years (generally). This is a complex topic with quite a few complicated rules, options and elections, as well as very specific guidelines. Depending on the total cost involved, the options chosen regarding depreciation can significantly impact your taxable income in the current year as well as future years.
If these scripts are purchased for resale to your customers, they should be included in "Purchase for Resale". If they are integrated into a solution you build for a customer, "Materials Purchased" would be a more appropriate category. Both of these categories would be reported in the "Cost of Goods Sold" section of the tax return.