R1: repair
By the time a leak shows on the inside of a building, the water has already been in the roof assembly for a while. Left alone, it works through insulation, stains drywall, warps ceiling panels and eventually brings a section down. On a commercial building that means ruined stock and interrupted work; in a house it means a bedroom ceiling on the floor.
Repair is the first R because catching a leak at the flashing, before it reaches the interior, is the cheapest roofing work there is.
Where roofs actually leak
Almost always at what the trade calls flashing conditions: any place the roof changes direction or something pokes through it. Air conditioning curbs, exhaust vents, skylights, chimneys, parapet walls, and the junction where a lower roof meets an upper wall. The open field of a roof, tile or shingle or membrane, rarely leaks on its own.
That is why my inspection spends most of its time on the transitions and not on the middle of the slope.
R2: re-roof
Re-roofing means a new roof covering over the existing one, or for tile, the same tiles reset over new underlayment. It suits a roof where the deck is sound, there is only one layer up there, and the surface has aged out but nothing underneath has rotted.
It is faster and cheaper than a full replacement, but it is not right for every roof, and I have a blog post on the conditions that have to be met.
R3: replace
Full tear-off down to the deck, repair of any bad sheathing, and a complete new system from drip edge to ridge. This is the answer when there are already two layers, when the deck is soft in several places, when the original installation was wrong enough that overlaying it would just hide the problem, or when you are changing material entirely.
It costs the most and lasts the longest, and it is the only R that resets the roof's clock to zero.
Choosing
Repair if the damage is local and the roof has life left. Re-roof if the surface is finished but the structure is fine. Replace if the structure or the history says nothing else will hold. I give the verdict in writing after walking the roof, and if it is a close call you get two scopes to compare.
The worst choice is none: a roof left alone in this heat and wind picks its own R, and it is usually the expensive one.