I'm just going to assume you didn't read a single reply on that last two pages, which pretty described that we've been genetically modifying food for thousands of years. Hell, there's no reason genetically modified food can't also be grown organically.
Ah I think there's a misunderstanding. You refer to species that have gradually been bred. That's a natural genetic modification.
means is genetically manipulated/engineered stuff. That one is built within one generation by using vector-DNA (also nicknamed jumping genes) as a vehicle to insert totally foreign DNA into an organism.
[digression: a very general and lay-ish explanation of how this works:
You cut out the gene you want to insert into the target organism and attach it to a vector gene. The vector gene is like a taxi that brings your gene into the target organism's cell core.
It cuts open the target's DNA in a random space and itserts itself and the new gene into the DNA. Repair enzymes detect the broken DNA-chain and close the gap, most of the time overlooking the fact that a new bit of DNA has been inserted. Often the new DNA is in a wrong place and simply creates an indecipherable muddle which often causes no harm. In other cases it can lead to cancer or cell death. Very few times it happens to be in a place where it gets properly read and decoded. Then your gene manipulation was successful.
Vector-DNA appears naturally and is a means of some viruses to transport and insert their genetic information into their host's genome to force it to build more viruses.]
The problem with vector-DNA is that it jumps not only into the genome when you want it but also jumps out of it and inserts itself into a different organism without any warning (hence the nickname jumping genes). Vectors are totally unpredictable. That's what makes them so dangerous: if you eat them, you may end up with no damage to your own DNA. Or you might end up with a tomato-flavoured tumor.
With the classical Mendelian breeding there is no such danger as this kind of enhancement works with totally stable genes that stay in their places. Hence such food is safe to eat.
Btw, over here in Germany, genetically engineered ingredients must be listed on a product. Genetically engineered fruit or veggies don't get sold at all as there is literally no market for them. Consumers here are strongly opposed to that stuff and would boycott its sales.