So, the problem is that you think dpi is a fixed size. It is not.
If you screencap something, it has fixed pixel dimension, but the "72 ppi for a screengrab" is sort of a hack: this is obvious when you consider that the "i" in ppi means "inches" and that there are 1080p 13 inch monitors and 1080p 50 inch monitors. Exact same pixel dimensions, different physical size.
For a PDF, though, the program is primarily aimed at physical printouts, so there is an specified physical size to reckon with, and the typical rule of thumb is going to be 300dpi/ppi (printed/downsampled; note that dpi and ppi are different but similar enough for informal conversation).
A 1920 x 1080 screencap unresampled (unaltered) is only suitable for about 6.5 x 3.5 inches. If you drop it full-size onto a letter-sized paper, it must be upsampled (or worse: stretched), and this results in a quality loss. This is the resizing that @billy Kerr mentions.
Aside from this, zooming any image on a screen is going to result in some loss of quality, and your pdf zoom level is not going to be faithful to the printed version. The 100% screencap is native resolution, the PDF is simulated, and often the 100% page size does not align with a physical ruler anyway.
So the short answer is: set up your PDF print size to be exactly px-width/300 by pix-height/300 inches and your images will not be resized or resampled.
Further: ppi is a flag set in the headers and is really only a recommendation. Not all image file formats even support the ppi flag. Only the pixels in are actual image data.
Do a deep-dive on ppi on this stackexchange and you will find more tangential discussion about dpi/ppi. Look especially for the term "effective resolution."