Biologically I think there is only one way that all daylilies rebloom. That is because the scape in daylilies is what is called a bostryx. A bostryx is a sympodial inflorescence and what that means is that the apical meristem is terminated when a scape is produced and growth is continued by one of more axillary meristems. The apical meristem is consumed to make the scape.
I begin by looking at a daylily when it is still small, immature, a juvenile fan & crown that cannot bloom. There will be a vegetative meristem (growing point) - the shoot apical meristem, in more or less the centre of a one fan crown. It grows (increases in size) and while doing so splits off part of itself as new leaves - first on one side and then on the other and then back on the first side and so on.
After it has grown enough it stops growing in size and stops producing new leaves and now changes to a reproductive meristem. It now produces the scape and its branches and all the buds. It is no longer growing so it gets used up as more and more of it becomes parts of the scape and flower buds. The fan will still have green leaves and it will have a scape but to produce more new green leaves one or more axillary meristems must sprout.
When a daylily reblooms, what happens is that the axillary meristem grows sufficient new leaves fast enough to produce its own scape in the same growing season. In a daylily that does not rebloom either the axillary meristem does not start to grow in the same growing season or it does start to grow sometime during that season but does not grow enough to produce its own scape. That will usually mean that the meristem will continue to grow in the next growing season - that is, it will produce some green leaves and a scape in the next growing season.
The seemingly different patterns of rebloom appear because of the amount of time that can pass once the vegetative meristem becomes a reproductive meristem and what happens during that time to the developing axillary meristem.
Pattern 1 - this happens in my growing conditions to 'Heavenly Harmony'.
The axillary meristem develops into a bud and the bud does not sprout until closer to the autumn and the leaves of the initial fan yellow and die. There is no rebloom. No new leaves appear after the scape appears but the leaves remain green and their normal full length all summer. All summer there is a fan of green leaves with a central scape.
Pattern 2 - this happens to 'Ophir' in some years in my growing conditions. In other years 'Ophir' follows pattern 1 (for some unknown reason) and if I change the growing conditions it follows pattern 3 (when I supply it with high nitrogen fertilizer).
The axillary meristem develops into a bud but the bud sprouts relatively quickly after the scape first appears. One can then see the long mature length leaves of the first meristem & fan and long mature length leaves of the axillary meristem (now the new shoot apical meristem) separated by one or two short 'leaves' that are daylily bud scale equivalents. The new shoot apical meristem stops producing new leaves some time in July and its leaves remain green until October. There is no rebloom.
Pattern 3
The axillary meristem develops very quickly. It does not develop into a bud. Growth of new leaves continues without an obvious break in time (there may be one slightly longer delay between the last leaf of the first meristem and the first leaf of the second meristem but one would need to be measuring temperatures and the length of delays between the leaves carefully to notice it). There are no obvious bud scale type leaves that are shorter in between the regular leaves from the two meristems. The leaves of the two different meristems appear to have been produced by one meristem continuously. The new shoot apical meristem does not stop producing new leaves until it produces its scape - that is the second scape from this crown and it is a rebloom scape. Although the two scapes appear to have been produced by one fan they have been produced by two meristems and in reality by two different fans.
If there is another rebloom scape then pattern 3 is repeated.
The visible patterns of growth and flowering are determined more or less by how quickly the axillary meristem develops and when it starts to develop in relation to when the shoot apical meristem is promoted to a reproductive meristem. In some daylily cultivars, in some locations and in some growing conditions the axillary meristem has already become a bud in the autumn. In those cultivars one can dig up a crown and look at it late in the year. One will find a bud. If one removes all the leaves from that bud then inside it one will find a central tiny scape (may need a microscope in some cultivars to see it or not if it is late enough in the year) and right beside the tiny scape either one or two tiny buds. Those tiny buds are the axillary buds, one of which will be promoted to sprout in the autumn of the next year in pattern 1. Much of what appears in a daylily growing season for some cultivars in some growing conditions has been prepackaged a substantial time before and is ready to simply unfold.
A daylily fan ends its existence when its meristem becomes (more or less) the scape.
