Once you start creating transactions you start to realise that in a month, the same kind of stuff always comes back. For example:
Going out for drinks
Like wise, you should start to notice that you always spend the same amount of money on these things. That amount may be too high for your tastes, and you may want to change that. Or at least, keep track of it.
These things are budgets. Budgets are a kind of "category" that come back every single month. Bills are returning (rent, water, electricity). You buy groceries every day. You need to pay rent every month.
In what is called an envelope system you stuff money in envelopes and spend your money from those envelopes.
Firefly III uses this method, which means you can create "envelopes" for any period. Example: € 200,- for "groceries" or € 500,- for "bills" every month. On the budgets-page you can create budgets and set envelopes each month (or each week or year). Expenses can then be assigned a budget and you will see on the budget page how well you are doing.
There is even a special budget report.
Firefly III also features categories. These are also interesting and useful, but slightly different.
If you try to save money every month on a certain subject, it's a budget. Groceries are budget. Bills are a budget. If you travel by train occasionally, it's not a budget.
First and foremost: a category is "incidental". You don't buy new furniture every month but you might want to keep track of such expenses. Or you don't care about costs for public traffic (budget-wise) but a category would be nice.
The rule of thumb is: would you make a real life envelope for it? If yes: budget. If no: category.
Categories can be used in deposits (earning money). Budgets cannot.