A VARIAC is an autotransformer because it only has a primary winding that operates by self inductance; there may be several physical taps on the primary, or a wiper on the primary, that creates the secondary voltages. When I first came across an autotransformer, it was confusing for me to think that a section of the primary winding was simultaneously acting as the secondary winding depending on the tap location, which is only a solder connection to the primary. There is no physical separation between the primary and secondary windings. Consequently, the secondary AC return will still seek ground just like the primary AC side - and is an electrocution hazard.
In contrast, an isolation transformer operates by mutual inductance where the primary and secondary windings are physically separated, and where the only connection between primary and secondary is the magnetic flux linkage. Consequently, the secondary will not seek ground like the primary AC, instead, the secondary AC return is from one secondary leg to the other secondary leg, not between a secondary leg and ground. To get shocked you would have to touch both secondary legs at the same time. Because the secondary AC return is no longer to ground, you will not get shocked by touching either secondary leg by itself. In essence, your body becomes the same potential as the secondary leg that you are touching and no AC current flows.
I have done a lot of experimenting with transformer operation, but I an concerned that someone might try to duplicate my demonstrations who are not experienced and may hurt themselves, so I'm refraining from talking at great length about electronics techbench isolation transformers.
I am not suggesting that you try touching the secondary legs of transformers. I am only describing why an isolation transformer is sometimes called a safety transformer. But we all know that electricity kills if you don't know what you're doing.
Autotransformer gets its name from AUTO, which is Greek for SELF; like AUTO-Navigation that means self-navigating; AUTO-motive that means self-propelled; and AUTO-transformer that means self-excited transformer.