They can pay themselves a wage, which is a business expense, and then save their wages like everyone else.

Your teashop friend could just as easily pay themselves to run their shop and invest whatever is left into the shop. Profit isn’t necessary.

I find it confusing. How do you differentiate if that is a "wage" or "profit"? How does a person who owns a small business determine how much wage to pay themselves with? I would think most small business owners will just put enough money into the business expenses for how big they want their business to be, then take the rest for themselves.

A small business typically don't need as much money to reinvest back into the business itself unless they are looking to expand the business to something bigger. There is only so much you can spend for business expenses when you don't want to deal with expanding your business even bigger. Some people only want to own a small shop.

For example, my friend at the tea shop is happy with the size of their small shop. They already offer enough stock to locals. They don't want to expand anymore. She loves running a tea shop and talking to locals, but does not want to deal with running a big store with employees. But from what you're saying, they should keep reinvesting in the business, even though the business doesn't need more money to avoid making a profit.

I understand profit is an issue with bigger companies due to them stealing money from their employees by paying themselves much more, but I am trying to understand how profit shouldn't exist for a smaller / mom and pop / 1 person shop.