Ah ..... Mmmm... I don't think that's correct.
I think "retread" means ALL of the ways that worn tires get renewed so they are reusable - and there are 3 methods:
1) Recap - where the old tread rubber is buffed off, new, uncured rubber is added, and cured in a mold that only molds the tread area. The original casing is visible and readable, so the original manufacturer and date can be determined. Usually there is a number branded in the sidewall to indicate who recapped it and when. In tires designed to be retreaded, there is a black space designated for these numbers.
2) Remold - where not only is the tread rubber buffed off, but so is the sidewall. The original casing information (including the size) is no longer visible - meaning only what the retreader has in the mold is visible. These would including coding so the date and retread manufacturer are indicated, but the date and manufacturer of the original casing is not (but there might be a way to figure it out - barcode?)
3) Precure - where the tread rubber is buffed off and a precured tread is cut to length and cured onto the casing. The original date and manufacturer of the casing is visible, but there is coding so the retreader's information (including date) are indicated. The advantage of precure is that less heat is put into the casing, the retread rubber can be made of better, harder to process rubber, and is less expensive than the other methods. The disadvantage is that there is an obvious splice (discontinuity). It's more of an appearance issue, not a performance issue. Bandag and Oliver are 2 manufacturers who come to mind.