Yep, hybrids are normally the result of crossing 2 distinct and stabilized varieties that belong to the same species.
Most big company hybrids are the result of crossing 2 inbred lines to get very uniform F1 hybrids
Old fashioned personal hybrid F1's are the result of crossing 2 varieties that are not usually inbred lines.
Most normal hybridizing does not leave sterile F1 plants, and when done in a natural way, seeds from the F1 can be saved and grown as F2 plants, which will all have different combinations of characters of the 2 original varieties crossed, mostly all different in some ways from the F1. Some of the F2's can be even more special than the F1, especially if the original varieties crossed were normal open pollinated varieties.
Most vegetable varieties available have always had some hybridizing in their ancestry. Yes, even heirlooms. Heirloom growers should not be adverse to normal old fashioned crossing of open pollinated varieties.
=====
GMO varieties on the other hand are varieties and hybrids that have ARTIFICIALLY INSERTED genes in their nuclear DNA, the DNA in the chromosomes. These artificially inserted genes come usually from entirely different organisms such as bacteria or fungus. Those gene/snipets are often altered chemically first, then reproduced in a lab. Once the gene fragment is made uniform and is concentrated, it is then inserted into an inbred mother-father self fertilized seed. For a hybrid GMO, they will do the same for the other inbred parent line. Thoise are then grown and increased into large numbers, most of which will be waste, or maybe used to make compost or animal feed, until just the right parent lines are made. The parent lines are then crossed, and the GMO gene fragment remains.
A few of the GMO things done with corn are:
The inserted gene or genes are used to
make the corn tolerant of roundup
and/or
make the corn plant make its own fungicide that stops things like corn smut.
=====
GMO= not natural
Hybrid= usually natural, but can be done unnaturally
An example of unnatural hybridizing is Brandy Boy F1 hybrid tomato. Breeders cross 2 inbred lines. (inbred lines in tomatoes is not by itself unnatural). One of these inbred lines, the one to become the female parent, is a line that is selected from a long older previuous breeding program where breeders developed a variety that makes no anther cone. Having no anther cone makes the skilled work done by people in India a lot easier. In the case of Brandy Boy, something happens in the genetics so that all the seeds that someone might save from the F1 grow out into plants that make horrible rotten tomatoes because something goes wrong with the pollination and seed development inside the F2 tomatoes.
Effectively, Brandy Boy has an EXTINCTION GENE in it, but do not be confused. The extinction gene here is not from artificial gene insertion. It is from first breeding a variety of tomato that makes no anther cone, which I guess was originally a natural mutation.
Saving and breeding such a natural mutation, which would normally soon itself die off, is an unnatural thing. Plus the effect of it that causes some of its descendants to have extinctiuon gene is considered an extra bonus to the big hybridizing companies.
=====
Editting to add:
Yes, nature can and does GMO's. It is true. They are seemingly random events, and are done by certain Viruses and Bacteria. In fact, scientists use these bacteria and viruses to do the gene slicing and splicing. An example of this in nature is found in the genes of Blackbirds. Strangely, a large percentage of their space filling DNA, the parts that do little or anything other than fill space on the strand, is the same as Trout DNA. Bacteria has been transferring DNA across these 2 species for a very long time.
