Being free to spend money on the things that matter to you as much as you can is the goal of a good budget.
There are apparently many different named “categories” or “types” of budgets. I am not going to even try to distinguish if there are different types in my approach.
For one, it seems that there are multiple, overlapping names of different things by different parties; meaning there is not really a standard naming scheme. And secondly, how you personally achieve your money goals depends on how you personally have to handle money — it doesn’t matter if it works for me, if it couldn’t work for you, but maybe you understand the idea, and adapt it to your needs.
A budget is the sum of finances allocated for a particular purpose and the summary of intended expenditures along with proposals for how to meet them. It may include a budget surplus, providing money for use at a future time, or a deficit in which expenses exceed income. 
- Income budgets are slightly smaller than the real income.
- Expense budgets are slightly higher than the real expense.
- Cashflow at the end of the month has to be positive.
- Always have at least one month income buffer
- We are interested in the overall picture. Every week could be different, but over the year it should make sense.
- Income: Everything you earn at your job, gifts, dividends, …
- “Hard” expenditures: Rent, utilities, … everything you have to pay, that is basically out of your control.
- “Soft” expenditures: Food, gifts, … things you need, but are more under your control.
- Long Term Savings: personal retirement provisions
- Short term savings: bigger financial spending (vacation, bigger subwoofer, …)
- Buffer savings
- Fun Stuff: Books, Games, Music, Movies, …
Income and Expenditures are at least predictable and can be budgeted. Just check what always has been, and think about what is going to happen. Gifts can also be budgeted: you know when people have birthdays, and what gifts are expected.
Long and short term savings can be automated. For short term savings just use a suitable second account (for example “Tagesgeldkonto” in Germany). If you do not want to automatically invest in your long term savings (you should), then you could also just transfer this temporarily to a different account.
Buffer savings don’t need to be much. They are just there, to get to a positive cashflow every month. If there is enough buffer savings, this budget can be removed for the time being, and spend on other things.
Which leaves the remaining budget for fun stuff. This fluctuates a bit, because peoples birthdays are not regular, or some other expenditures are not every month. There are two ways to deal with this: use what you have for the month. If it is less, then it is less. Or calculate the average for every month.
There is a reason you should have a buffer on your main spending account, and under-budget income respectively over-budget expenditures, and have dedicated buffer savings.
At the end of the year, we want to have maximized our goals in term of savings and fun money, while also don’t have to be stressed about paying the bills.