The two are closely related. A budget is a goaldetailed plan for how to spend, keeping track of spending. Expense tracking is a tool to analyze your previous spending performance.
A budget isCreating a plan for how much money to spend. A budget your money without any record of your previous spending is--is an empty promise to yourself that you will never follow up on. A budget that isDid I stay within my budget? Doesn't matter, I didn't track the spending anyway. Even if you do plan to track your performance, if you have not based on previous spending is unlikelypreviously done so, you won't have a good basis for how much to succeed consistentlyexpect in each category.
Most people have a general idea of how much they have spent and many budgets are formed based on that general intuition, but they are often surprised when they track how every penny is spent and look at the totals from month to month and over years. By actually seeing how much has been spent it's easier to pick the big financial drains and target them for reduction, if your desire is more savings, for example.
I know people who keep a close eye on what they spend each month, but they don't allocate money in categories for the next month. They don't perform as well on reducing spending, but they often don't care. They feel like they make enough and they save enough, so why worry?
I also know people who create an unrealistic budget each month because they haven't done a good job tracking their previous spending. They know what the monthly bills are, but they don't account well for variable or cyclical expenses like repairs, Christmas, etc.
Both tools are essential for maximizing your own personal finance.