Adding to what others have said, I do think tuvar / toor / tuver has a slightly more distinctive flavor / aroma.
Oiled dal is obvious - oily and darker. It’s unusual to find outside an indian store.
Do you soak your lentils as a matter of course? I always do, and change the water at least once especially with heavier / harder to digest dals (toor, urad) and all beans. I won’t eat unsoaked versions (assuming I know - I have reacted after eating them when I didn’t know).
I do not discard cooking water after this, rather adjust the amount of water I add for cooking according to the consistency I’m going for - 1:1 for thick, all water absorbed, 1:2 for a thick dal that can then be diluted as needed. Almost always pressure cooked.
In terms of aromatics, I don’t have an issue with using raw onion / garlic - many recipes call for dal to be pressure cooked first with raw onion / chili / ginger / garlic, and tempered later with more of the same plus spices.
It is entirely possible you just don’t like toor dal or are sensitive to it. I have family members who discovered they are allergic to toor but not anything else. Of the “daily” dals - yellow moong, red masoor, toor - toor was considered the heaviest and hardest to digest, which in modern parlance may mean that there is broadly a higher risk of sensitivity / allergy.
