"In Numbers it would seem that the Header and Footer "ribbons", or whatever Numbers calls them, are only visible when you go into print mode. "
Numbers gives them the same name as they have in Pages: Header boxes and Footer boxes, Header in this context being short for 'running header', a space at the top of each page that carries the same text from page to page through the whole document or through a Section (or Chapter) of the document.
In Pages, these headers and footers, if used, are always visible on each page (with exceptions where the user/author has chosen to not show them (usually on the opening page of a chapter).
In Numbers, pages are defined ONLY when the user is Printing the document or Preparing to Print. When editing the document, there are no 'pages,' and the 'page headers are hidden,
Header boxes and Footer boxes contain only entered data, with one exception: A page number calculator can be placed in a Header box or a Footer box, where it will calculate and display the page number of each page (in Pages), and the page number of the page to be sent to the printer in Numbers (when in Print Preparation or actually printing).
Table Header rows contain Header cells. Those cells can contain entered values (eg. Column and Row numbers or names, or formulas that calculate and display values depending on values in other cells on the table, or on internal sources, such as the system clock and a Formula consisting of the TODAY function.
Here's an example:
The yellow filled cell is in a Header row. The other two cells in that row are empty, have had the 'header grey' fill changed to No fill, and have had the upper and vertical cell borders removed to leave only a single cell visible in the row.
The first screen shot shows a section of the table in Edit mode, taken on Nov 22, 2022.

Pressing command-P changes the screen to Print Prep mode. Pages appear, the running header text appears on each page, Table Header rows (1 and 2) are repeated on each page, and the page number of each page is shown in the Page Footer's centre box at the bottom of each page.

After taking the screen shots, the document was closed, and saved to the Mac's data SSD.
More to follow…