Rule of thumb: The formula bar shows the same date format as number format "General" would do but with 4-digit years.
For perfect confusion, every single cell and every cell style has a "language" setting in the number format settings which should be labeled "locale" since it overrides the global locale setting mentioned by robleyd. You can change the number format locale together with the input behaviour for every single cell.
The "Default" language/locale that is shown in the number format dialogs is the global one from the options dialog. And yes, it affects the formula bar as well.
- Number format dialog with locale "Default - German (Germany)" following the locale setting in the global language options
When I write something numeric into an unformatted cell, the cell's language/locale reads "Default - German (Germany)" because that is my global locale setting and the cell input recognition behaves German with decimal 3,14, € currency by default, 31.12.1999 dates and more.
When I send that document to Moonwalker, the same cell gets a language/locale that reads "Default - English (USA)" and the cell behaves accordingly with decimal 3.14 and 12/31/1999. Same with the "Default - English (Australia)" except for the 31/12/1999 date.
If I want to look my cell content always the same, I need to switch to an "explicit language/locale" without the "Default -- " prefix.
This crude concept of "I don't care, just use the default language from my global setting" would not work well with currency symbols. My € must not switch to $ on your computer. Currency symbols are handled separately and do not change with the locale.
The spiral of confusion has another turn: numeric constants in a formulas always follow the global locale.
3,14 with a decimal comma changes to 3.14 with a decimal point when switching the cell's language/locale and you've got to enter any constant value in the same way.
However, the formula =3.14 always works with a global point locale and =3,14 always works with a global comma locale.
With a global locale "German (Germany)" and some English number format language/locale, I have to enter 3.14 as a constant value but =3,14 in formula context.
Since this started with dates: if you install LibreOffice, you can define which patterns should be recognized as dates but this does not make things any easier. It is just another source of confusion. For instance, this customization is reset to defaults when you switch the global locale setting.