There are different kinds of text that can be added to a Map window, such as automatic labels, custom labels, and text objects.
With automatic labels the font size does not change as you zoom in and out, so if your font size is nine (9) point when zoomed in to the map, then it will still be nine (9) point when you zoom back out. Your screen metrics determines the size and position of automatic labels on the Map window, which is not an accurate representation of what the printed map will look like. As an example, you may see two labels near each other on the screen while overlap detection is turned on, but only one of the labels displays in your printout. This is because the size and position of the label changed after applying the printer metrics, which caused one label to overlap the other label.
Custom (or edited) labels are sized the same way as automatic labels: their font size does not change as you zoom in and out. However, custom labels are always drawn, so they appear in your printout.
The size of Text objects does change as you zoom in or out on the map. The font size scales to make text appear larger as you zoom in and smaller as you zoom out. Text objects, like other map objects, always print.
To have the screen mirror your printout when the map includes automatic labels, put your map into a Layout window. The Layout window uses the printer metrics, so that you know what your printout will look like (and you will know what labels will be on the printed map).
See also, Viewing and Printing Text in a Layout.