I agree that what people call it isn't important, what does matter is that you try run your finances further ahead than payday to payday and recognise that there are ups and downs in income and expenses that you should try and anticipate, such as:
insurance, Christmas, holidays, school shoes and uniforms etc etc
things that break, eg cars, appliances, teeth, pets etc
loss of income due to illness, redundancy, desire to stop working or reduce hours/level of job
savings to support DC at university or house deposits if applicable
big costs like home improvement or car replacement, which you should aim to cover by saving not borrowing where possible or if you do borrow, should be as small/affordable as possible, ie don't take out a £500 pm car lease if you have no emergency fund or would be screwed if you lost an income.
So you need to plan for all the above out of monthly income and ensure you don't see what comes in each month as available to spend by the next payday.
Of course, you could come to a point where you have plenty of money saved and then you can think about retiring/spending more/working less. Obviously many people want to pass on money to their children but there's also a school of thought about 'die with zero', ie aim for your money to last until the end of your life but not have loads left over because you've saved or done without for no direct benefit to yourself.