Thanks to all - I think I'm starting to get an understanding of this. But can LR change the print size without changing the number of pixels in the image so that the image can be either compressed or stretched? I've been looking at the various panels and also at the Martin Evening and Kelby books and do not see how to do it.
When choosing a paper template, it has the paper dimensions, the print setup, and 1 or more frames defined. The frame is the image placeholder. The right panel in LR shows you the dimensions of this frame.
LR placs the image in a placeholder and thus adjust the image size (compresss or stretch) to fit into the frame.
In the colormanagment options, you can specifiy also the ppi value to use. Note that ppi is pixel per inch(on the print!),
whereas dpi is the number of ink-dots the printer uses per inch to print, regardless of the ppi setting.
The dpi is a given of the printer and can be set in the printer dialog panels.
Printer brands use a default ppi for their optimisations, HP is 300ppi (a multiple of 150 actually), Epson is 360ppi(multiple of 180 actually). So depending on your printer you just set it to this default/optimised value.
I use 300 for my HP. This is regardless of the physicl size of the actual print.
Note: In the (recent) past printing functions where not very optimal, and deviating from these optimal values could introduce moire like artifacts. I do not know if this is still the case, but i simply stick to the default optimal ppi settings for given printer brand, better safe than sorry here.