These two words get used interchangeably by cleaning companies, but they describe different problems and different processes.
Cleaning removes surface soil, residue, and buildup. It works on grout that has accumulated grime but has not been permanently altered. It works on tile that has soap film or light mineral deposits. Done correctly with the right chemistry and extraction, professional cleaning produces a visible improvement and extends the time before a deeper intervention is needed.
Restoration addresses damage that has worked into the surface. Etching on marble or travertine — the dull, slightly rough marks left by acidic contact — cannot be cleaned away. They are physical damage to the stone surface and require mechanical correction through honing and polishing. Grout that has absorbed permanent staining or deteriorated past the point of cleaning may need color sealing or replacement. A topical coating that has failed and begun to peel needs to be fully stripped before anything else can be applied.
The distinction matters because using a cleaning process on a surface that needs restoration produces a disappointing result. And using a restoration process on a surface that only needs cleaning is unnecessary and more expensive. A proper assessment before the work starts is the only way to know which one applies.