First, thank for you previous reply which clarify the ppi, because resolution often confuses people. ppi is useful only to calculate physical printing area of a picture, if you give number of pixels and resolution instead of forcing print area. Changing this value for photo print has no meaning, has you constraint the print size.
You don't need to constrain the print size though.
I just opened ps and understand why my words are confusing you.
PS do not use 'resample' term as other softwares (and I) do.
Ps uses the correct terms
With resample checkbox unchecked you only change the ppi information field (and again, yes, it's only a field, it does not affect image data)
You can change print size and ppi (as you amend one the other changes automatically.
With resample checkbox checked, the number of pixels is changed, a filter is applied to get the new picture.
Yes that's correct. It's also called interpolation.
I try to sum up here my minds (and what can be found in a non-ps world

)
- resize just remove (when reducing) or clone (when enlarging) pixels to get the new image. This is very fast, generally used for preview only and this does not exist in ps.
Not sure that is correct? You can certainly do anything in Ps regards adding canvas or deleting pixels (cropping) without resampling. But I'm not 100% sure what you mean.
- resample create new pixels, calculated by applying a filter to the original image pixels, this is in ps.
You can do this in Ps yes.
I hope I clarified. :???: not easy to do it in english.
I'm struggling to understand your thoughts exactly. You can increase the print size by reducing the ppi of an image and conversely you reduce the print size by increasing the ppi.
By adding or subtracting pixels by you are changing the number of pixels in the image therefore in my mind you are resampling. Although I do see that if you crop off pixels or add pixels by increasing the canvas size, you'll not resample the image - but I am not talking about this above (or below)
Use the equation I provided
Pixels (P)= Resolution (PPI) / Print Size (PS)
So lets try a couple of things.
I'll use my 20D image files here which are 3504 pixels x 2336 pixels.
When the come into Photoshop, generally they are displayer as 48.667" x 32.444" @ 72ppi. This is exactly the same as 35.04 x 23.36" @100ppi or 11.68" x 7.7867 @300ppi.
Multiply the PS x PPI and you'll get the number of pixels. So from this you can edit to almost any size without changing the number of pixels in your image. Obviously if you want to print around say 24 x 16 (which prints at 146ppi) or larger, then you may want to consider resampling a bit but even at 146ppi you'll get a quality image that will look great on a wall.
Does this help?