I've got a tile shower that is original to the house (so 1975) that really needs to be refreshed, the tile is not the best color and the groute is discolored or missing in places.

For example, front cement step discoloration, meaning one step wasn’t matching the other two cement steps.

It will soak in the underlayment and discolor the floor.

It is currently on the market and sold, however, the buyer backed out after the home inspector found some discoloration (was not tested for mold) in the attic.

While re-reading the property description, I noticed the above note: 'Property may have discoloration', and I have no clue what this means.  

The backyards of the surrounding neighbors though, didn't look very nice. 3 out of 5 had sheds in their backyards that looked like they were falling apart, and one of the sheds was almost as tall as the house. 2 out of 5 also had a canopy/tent type thing and they both were discolored with holes in them, but they were still propped up.

"Yesterday we were cleaning the garage and noticed some discoloration on the ceiling.

They are telling you there was a "discoloration, that may, or may not, have been mold" and letting you know that no mold remediation was done, in other words....."

Roofs often get discolored just because mildew (or whatever it is scientifically?)

If there is discoloration in the wood pores then you can do a light sanding, HEPA vacuum, wipe with the soap/water solution, allow to dry and HEPA vacuum again.