After H. V. Wilson's discovery of sponge cell reaggregation and sorting out, Julian Huxley repeated Wilson's method using different species of sponges (that happened to have larger cells) and Huxley concluded that sponge cells rearrange according to differentiated cell type.
Wilson himself concluded that cells were either re-differentiating to different cell types, depending on geometric location, or (Wilson later believed), being replaced by previously undifferentiated "archeocytes" (which would now be called "stem cells").
Notice that this same set of alternative explanations also apply to salamander leg regeneration.
Specifically, are the regenerated ulna, radius, carpal, and phalanges made by rearranging chondrocytes that had previously been part of the humerus? Yes. (And also by some cells that had been dermal fibroblasts.)
Are the regenerated muscles made out of cells that had been part of the triceps, biceps and other proximal muscles? Yes.
Also notice that people do not usually consider that limb anatomy is produced by rearrangement of cells that have already differentiated (or already become committed to becoming chondrocytes, or becoming muscle cells, blood vessel cells, pigment cells, nerve axons, skin cells). Instead, undifferentiated "stem cells" are assumed to choose which cell types to become, based on their geometric location.
(Theoreticians of "Reaction-Diffusion Systems" versus "Positional Information" advocate alternative methods by which chemical signals could cause each cell type to differentiate at the correct locations.)
These theoreticians are not concerned with methods for moving differentiated cells to correct locations, even though that is how at least half of development is accomplished. Their theories are designed to explain phenomena different than what actually occurs. (Imagine ancient astronomers debating alternate explanations for the flatness of the earth's surface. That's the situation in theoretical embryology.)
All skeletal muscle cells, pigment cells, blood vessel cells and axons began differentiation at locations distant from the limb buds, and have to crawl actively to reach the limb buds, where they arrange themselves into correct anatomical patterns.
Only the geometrical pattern of the limb skeleton is produced by causing mesodermal cells to differentiate onto chondrocytes at the correct locations (forming the humerus, the radius and ulna, the carpals and the phalanges).
Regeneration of Platyhelminthes (Flat Worms) also uses rearrangement of differentiated cells.
If you create a branched head flat worm, by repeatedly cutting the anterior end in two, then the two heads will gradually fuse together. The separate masses of cells flow gradually back together, especially the muscle cells.
If two heads and two tails are caused to form (worm shaped like a + cross, with heads on upper and lower sides, and tails on right and left sides), then the heads and tails have no tendency to merge back together.