There is “GE” and there is “GMO”...I wish more was written about THOSE differences
In a way, those terms are meaningless. With or without human intervention, DNA is constantly mutating. There is no baseline that one can point to as the "original" DNA of an organism for comparison. It is the nature of DNA to change, of organisms to mutate. Each living human being has roughly 120 mutations that did not exist in either parent, and the same is true of every other living species as well.
If we restrict those terms to describing DNA alterations brought about by intentional human intervention, then "GE" (genetic engineering) would refer to the process, and "GMO" (genetically modified organism) to the result. Our processes for achieving these are extremely refined and targeted now, thanks to our increased understanding of the enzymes that organisms use to alter DNA. We extract and use those natural enzymes for our own genetic engineering projects. We're no longer limited the way our ancestors were, when they had no control whatsoever over what would result when they randomly swapped around thousands of genes between organisms.