Banal question: Is there a scientific theory in which the evolution of human beings and another kind of organism that have a common source means the same thing as when an organism evolves from humans?

As far as I know human beings and all other organisms do share a common source and evolution is a continuing process for all organisms, including man. That’s what the theory of evolution explains.

I’m not certain what you mean exactly by “means the same thing as when an organism evolves from humans”.

The word “organism” basically just means a living being.

A “human” is a member of the species “homo sapiens”.

Rutherford Hayes was a human organism.

Species are for the most part just taxonomic classifications scientists use to organize and classify organisms, but what actually exists are organisms.

Each cell of each organism has slightly different DNA. So, while most members of a species have many similarities in their DNA (usually but not always the same number of chromosomes, for instance, and many more detailed DNA similarities because they’re relatives of each other), their DNA also varies, not just from individual to individual, but from cell to cell, with the cells getting replaced, and every cell division potentially having some mutation of its DNA occurring.

Within a species and sometimes within an individual, significant DNA variations occur.

Whether or not an individual organism is different enough to be considered a new species, is an arbitrary decision for taxonomists to make. They generally don’t say that there is a new species unless they find a major variation that has, or has had, a sustained population. e.g. When an individual has extra body parts or is hyperflexible or gigantic or dwarfish or albino or has other unusual features – they just tend to say it’s an individual with unusual features.

So they typically never say, “oh look, an organism evolved from humans”. They say it’s a human child, possibly with some atypical traits.

Organisms do not evolve, populations of species do.