Charles Darwin came up with the term, "natural selection" to describe what he saw in nature and how his theories on the evolution of speciation developed. He compared natural selection to "artificial selection", which is the human intervention in plant or animal hybridization. Desirable traits and characteristics chosen by the breeder are promoted in hybridizing. Undesirable traits are discouraged from breeding programs. This term was later changed to "selective breeding". Therefore, these two terms are clear, a natural hybrid is one that occurs naturally in nature. An artificial hybrid is one that was intentionally produced through selection of the parents by the breeder.
It is easy to understand the origin of the hybrid when these terms are used correctly. Not only for the hobbyist but especially the taxonomist and biologist. The importance of natural hybridization is being recognized more than in the past. Clear documentation of natural Tillandsia hybrids; where they were found in nature and other species in their habitat is necessary. Many purists are not concerned about hybrids, only species. But a natural hybrid which originates in a mixed species population has it's place in the study of species.
We can't discuss hybridization without discussing one other type of hybrid. In your garden when a plant is found growing that you did not intentionally plant, or is not a native plant to your region, it is frequently called a "volunteer". The same is true in nurseries and private collections. Plants are growing in close proximity and the opportunity for hybridization is high. If one harvests the seed and grows it to maturity, chances are you will discover an "accidental hybrid". Only with an "artificial hybrid" (selective hybridization), or an "accidental hybrid (volunteer hybridization) is it possible to have a hybrid with one parent from Mexico and the other Brazil. This will not occur with a "natural hybrid".
I suggest that these terms be adopted properly. Lack of consistent terminology decreases the value of the hybrid. A "natural hybrid" is one that occurred naturally in nature. An "artificial hybrid" is one that was created by a breeder, usually through selection of desirable characteristics. An "accidental hybrid" is one that happened in a private collection, garden or nursery, but without intention. Alternatively one could adopt the terms, natural hybrid, selective hybrid and volunteer hybrid.