>thymus sweetbread vs. pancreas sweetbread

We made it to a family dinner at Incanto last Saturday after an unexpected delay.We toured the nearby old church of Mission Dolores (Mission San Francisco de Asis) and came back to the car to find the rear left tire flat. My very first. After a helpful visit from AAA, we were on our way, hungry and half an hour late.

I opted for sanguinaccio (fine-textured blood sausage) and the chef's special sweetbread. Mom is the only one who can't stand 'offal', so she went for house-marinated olives and halibut with greens. I now put 'offal' in quotes. Not only are these parts edible, they are increasingly prized by ordinary restaurants and diners. Incanto is known for plentiful offerings of uncommon cuts, and I was surprised to find only a couple of 'offal' options Saturday evening.
As I stretched my neck and belly to attempt to point to different types of 'sweetbreads', I became unsure of the exact locations of each. I had to come home to look them up.

Which sweetbread do you prefer? I think the name should be more specific, and I don't just mean the veal/lamb distinction. We think nothing of graphic-sounding names when we are used to them. 'Liver', 'pork belly', 'fish cheeks'... we might start calling sweetbreads by their real name - pancreas and thymus glands. 

...  (um) ...

Maybe not.