Patina is used to mean almost anything that happens to leather over time, including damage. It is worth being precise, because the difference decides whether you will like owning one of these covers.
On vegetable-tanned leather, patina is two separate things happening at once.
One: the colour deepens
Tannins keep reacting to light and to the oils on your hands. Undyed leather travels from pale sand to honey to amber. Dyed leather goes deeper and slightly browner rather than changing hue.
This is even and slow and it happens whether or not you do anything. Daylight speeds it up; a cover kept in a drawer barely moves.
Two: the surface compacts where you hold it
This is the part people actually mean. The spine, the front corner and the edge you open from meet your hand first, so those places burnish before the flat panels do. On brushed leather like Pueblo the fibres lie down and a low sheen appears. On smooth leather like Buttero the surface simply goes glossier.
The result is a map of how one person handles one cover. It is not designed and it cannot be copied, which is the whole appeal.
What patina is not
It is not a coating wearing off. A finished leather that goes pale at the corners is losing its surface, and that does not come back. Our hides are dyed through with nothing on top, so corners deepen rather than wear light.
It is also not damage. A cut through the grain stays a cut. A scratch on Pueblo is usually just the fibres lifted and settles under a thumb; a scratch on Buttero darkens with the rest of the panel over a few weeks.
How fast
Faster than most people expect at the contact points and slower than most people expect overall. Within a fortnight the spine of a Pueblo cover is visibly ahead of the back panel. The whole cover taking on a different tone is a matter of months, not weeks, and it never really stops.
If you want a cover that looks much the same at the end of the year as at the start, choose a dark Buttero and accept that it will still move a little. If you want the change to be the point, Pueblo on a trifold makes that change easy to see.