transgenic organism
A transgenic organism is one that carries a gene deliberately introduced from another source — often from a completely different species — woven into its own DNA. The added gene, called a transgene, becomes part of the organism's genome and, in many cases, is passed on to its offspring.
Making one means delivering the foreign gene into cells early enough that it ends up in the germline, so the whole organism (or its descendants) carries it. In animals this is often done by injecting DNA into a fertilized egg or by modifying embryonic stem cells; in plants, a soil bacterium that naturally transfers DNA into plant cells is a common delivery agent. The transgene typically comes with regulatory sequences so it is switched on in the right tissues.
Transgenic organisms are central to both research and application. Transgenic mice expressing a human disease gene let scientists study that disease; bacteria carry transgenes to brew drugs; and transgenic crops can be given traits like pest resistance. The defining feature is the addition of foreign genetic material — which distinguishes adding a gene from merely editing an organism's existing sequence in place.
Bt corn is transgenic: it carries a bacterial gene whose protein is toxic to certain insect pests, giving the plant built-in protection.
A bacterial gene living in a corn plant is transgenic by definition — DNA crossing species lines.
Transgenic specifically means a foreign gene was added. An organism whose own DNA has merely been edited in place — without inserting a gene from elsewhere — is genetically modified but not, strictly speaking, transgenic.