You can assign cost allocation tags to AWS resources. Each tag has a unique key and a value. Cost allocation tags can be used to track costs at a detailed level. Cost allocation tags appear on your cost allocation report. In this report, you can categorize and track your costs.
AWS Budgets is a service designed to create custom budgets. It can be used to explore and manage cost. It is however, not designed to track and categorize spending at a detailed level. You should use cost allocation tags track and categorize AWS spending.