I think the OP was asking about TIFF vs. JPG. Not sure how PSD got involved here.
Although others on here can give you a more complete answer, in short, converting to TIFF from a captured and corrected RAW file (edit instructions saved in sidecar XMP file) will result in the most complete picture file.
On the other hand, converting to JPG, from the same RAW file will result in a picture file that is in a reduced quality state. Even the first JPG conversion is a lossy process where picture quality is permanently loss.
So to print an image, a TIFF conversion is of higher quality than a JPG conversion (from the same RAW file) - which would result in the best possible print. Layers and other goodies just sweeten the deal with TIFF.
JPG is really a convenience file type for email, PowerPoint, etc. due to its smaller file size.
Tiff= Best possible image, but a larger file size.
JPG= Lossy, reduced image quality, but very useful in file sharing or when file size is a factor.