Yes it was, although it's certainly not limited to fax or low-res scanned images.
Tagged Image File Format. The "tagged" is what's nice about this implementation: the format includes many possible sections, each identified by a "tag" (a unique binary value). If a TIFF reader comes across a section it doesn't understand, it can simply skip over it, as each section contains a field which lets you find the next section. So it's very backwards-compatible.
TIFF was used a lot (still is used?) by places that do very high-resolution scanning, like for art books and the like. It's probably been replaced by other formats for the most part.