No, that's not how it would work. If you were somehow able to breed a cat and a dog, or better, a horse and a donkey, which can interbreed, you'd get a mix throughout, a mule. This is because every cell would contain both cat and dog genes. What we're talking about is when one of two things happens early in the formation of an embryo that cause some of the cells in the body (or fruit) to carry different genes than the rest.
One way that it can happen is when a single cell out of a very small number picks up an error (it's easiest to imagine only two cells) when it divides and is different from the remainder of the embryo. That portion of the embryo goes on to develop just as the remaining part does, with it's mutation included. Imagine it developed the genes for albinism. If that cell went on to form only part of the skin/hair/eyes, then only part of those systems would be albino, the remainder would be normal. This type of event is the cause of mosaic down syndrome as well.
Another thing that can happen is that one of a pair of fraternal twins can be absorbed by the other early in development. The two sets of cells develop into a single human, and both can contribute characteristics to the adult. I recall a medical show about chimeras in which a woman had some particular blood type (let's say AB) but her germ cells, and thus her children, had a different blood type (let's say O.) She had had a few kids, so it wasn't any sort of switched at birth scenario, just a weird event. The conjecture was that her whole reproductive system had formed from the cells of a fraternal twin.