A pixel is a pixel. Format makes no difference. If it's a raster image, it's always pixels.
Tiff is a common format for print because it supports many things other formats do not. (Or did not years ago.)
- Clipping paths
- High ppi
- CMYK color
- Internal lossless compression (if set)
- Universal format
- Embedded Color Profiles
Years ago (before the web) there were really only 2 widely used formats for images - TIFF and EPS (DCS was used but that's really just a bastardized EPS file). At that time, EPS more generally was used for vector graphics (although an EPS can be raster as well). Transparency for raster images had to be done via clipping paths. Only the Tiff and EPS formats supported clipping paths for raster images. In reality, only EPS supported clipping paths for several years. It wasn't until the late 80s or early 90s that tifs started supporting clipping paths as well. JPGs existed but they were always low resolution, used lossy compression, and didn't support CMYK or embedded profiles. Raster Image Processors (RIPs) did not support formats such as jpg or others when files were sent to the imagesetter. So no print file could use an image format which the RIP wouldn't accept. TIff and EPS were really the two formats supported by RIPs. And on older RIPs even Tiffs with internal LZW compression could be problem. Images basically needed to be a "vanilla" as possible to RIP well.
Today there are several formats which will work provided resolution is set properly. PSD, PDF, .AI as well as others, are now more widely accepted. This is especially true due to the move to a PDF workflow for much of print design.
You can easily use PSD and PDF files within an InDesign layout and the images are embedded in an Exported PDF properly for press. In fact, you can use RGB formats such as JPG as well and InDesign will convert the RGB to CMYK when exporting a PDF (if a print PDF format is chosen such as PDF/X).
But, speak to QuarkXpress users and you'll find you still need to stick to TIFF and EPS for the bulk of work because Quark doesn't have access to the integration code which Adobe controls. I, being primarily an InDesign user for press, personally, haven't saved a tif or eps file for many years, unless the file was being given to a QUarkXPress user. I much prefer the native formats of .psd or .ai. But QuarkXpress can't use those formats. (Although I think I read somewhere that the newer version of QuarkXpress can now deal with .psd files. To what degree, I'm uncertain.)
In the end, you're correct, format is far less important than the image resolution, color depth, and compression (if any). However, if providing "naked" or "bare" images to someone for press Tiff is still a very good format to use if the image does not have transparency. And a tiff with a clipping path is still better than a .psd or .png in that case.
Note that things in other formats have improved. You can now save a jpg with CMYK color and a clipping path. You just can't depend on that jpg when going to a press-ready format. But for transferring images jpg is a great format to use at times. For example, you can create an image with a clipping path and save it as a tiff. Then save *a copy of that image as a jpg set on "maximum" quality (don't use save for web) and that jpg will largely be identical to the tiff. The person receiving the jpg can then open it, and re-save it as a tiff. This is the basis for all the stock image sites and their high-resolution/clipping path images. One shouldn't continue to use the jpg, but for email or download the jpg can be drastically smaller in terms of file size. There may be some slight image color change due saving to a lossy format (jpg). However, as long as you use the "maximum" setting (12) you shouldn't see much difference between the tiff and the jpg.