Expenses, costs and payments are often used interchangeably as an expression of money leaving the company. However, conceptually there is a small difference.
An expense occurs when you acquire a product whether it is for resale, for production or for own consumption.
A payment takes place when you pay for the product.
A cost occurs when you consume the product, ie. when you sell it, when you use it for production or when you use it for own consumption.