What does PDF page size mean for your PDF?
Sizes are recorded in points, at 72 to the inch, in a box called the MediaBox. A4 and Letter differ by about 6 mm in width and 18 mm in height, which is enough to produce a margin of white or a clipped edge when printing one on the other.
Documents assembled from several sources routinely mix sizes and orientations. Resizing every page to one standard is what makes a bundle print predictably.
A page can also carry a CropBox, which is the visible area — trimming margins changes that rather than the paper size.
Why does a PDF print with a white band or a clipped edge?
Because the page is a different size from the paper. A4 is 210 × 297 mm; US Letter is 216 × 279 mm — wider and shorter. Print one on the other and the printer either shrinks it, leaving a margin, or fits the width and loses the bottom.
Most of the time you can leave the document alone and change the print dialog: Fit to printable area or Scale to paper size handles a one-off. The text comes out about 3 per cent smaller, which nobody notices.
Resizing the file itself is the answer when the document will be printed repeatedly, submitted somewhere that requires one size, or bound with other pages. Note that resizing scales the page as an image would be scaled — it does not re-flow text, so line breaks stay exactly where they are.
Mixed sizes in one document are common in bundles assembled from several sources, and are the usual reason a printed pack has one page smaller than the rest.