Film (like, for movies) originally had an aspect ratio of 1.33 (4:3), and this carried over to TVs and computer monitors. The image would generally be projected onto most of the screen, and if something was not to one's liking, the image could be adjusted with some knobs. Such stretching could be performed irrespective of the resolution emitted by the video card, and so, the knob(s) effectively changed the pixel aspect ratio (PAR).

If you take the IBM VGA 9×16 font as shown by DOS as an example, i.e. a 720×400 image, and project it onto a 4:3 area, you arrive at a PAR of 20/27. This font has a glyph core (average width and cap height) of 7×10px, and factoring in the PAR, its characters have an apparent aspect ratio of 0.51. That is to say, two characters would form pretty much a square bounding box (almost). This all will become important when wanting to faithfully reproduce that later.

The shadow mask/aperture grille of the CRT monitor would define the ultimate granularity of the visible image. The way I remember it, sharpness was never a concern. It felt dot-accurate even if it may not have been.

Anyway, LCDs have a fixed PAR (generally 1/1). Showing content intended for a different aspect ratio leads to an awkward situation. Untreated content appears squished, and scaling can only produce a pixel-perfect output if the factors of the resolutions match. With regard to the 9×16 font, the 20/27 correction is an awkward fraction; filling a screen perfectly would require a "10K" 4:3 monitor, and that is not going to happen, also because human vision caps out at around 300dpi (~a 4K monitor).

So what do you do? Design a new font. For example, if you take the VGA 9×16 font as a basis (in bitmap form), then, to reach the desired 0.51 aspect when presented on a 1:1 PAR LCD, you would add some pixels and elongate the stems. I present two examples of redesigns:

Toshiba machines had various LCDs, common were 640×480 and 800×600 (T3400 (1991) and 220CS (1996)), and there have been (for the time) unusual widescreen resolutions like the Libretto's 800×480 or the Portege 300CT's 1024×600. They showed 80×25 textmode with 8×16-sized cells, and the resulting 640×400 image was presented unscaled and centered in the screen. There was also a Stretch mode in the firmware. Sometimes, there seemed to be no/litle stretching artifact and sometimes there are hints of blatant Nearest Neighbor upscaling. (1)(2) The ROM font from the C&T Chips and Technologiges number 65554 chip is available in the int10h fontpack under the name Mx437 ToshibaSat 8x16. As said, the cell is 8×16 and the glyph core is 7×11px (aspect 0.63), making this font look comparatively tall over IBM VGA 9×16).

Second is a AST/CirrusLogic product such as the AST PremiumExec 386. I only have Internet images and videos to go off by, but it looks like it shows the 80×25 textmode with 8×19-sized cells. The glyph core is 7×12px (aspect 0.58). Perhaps they should have gone with 7×13px to reach 0.53, but there are some artistic constraints (and freedoms) everyone has got to bear/enjoy.

8×19?! Well, 8×19 multiplied by 80×25 textmode produces a 640×475 image, which fits nicely onto a 640×480 display, leaving just five unused rows.

Anyway, it is fair to say that 8×19-cell fonts were rare. VileR's only lists two 8×19 fonts in his database — and he surely has seen more hardware than me. The third 8×19 font to appear was around 1996 on certain Intel boards, which later would find its way into the Sun Microsystems x86 server lineup (e.g. the X4140), and then desktop motherboards as UEFI proliferated post 2006.