There is a term for it. It's called "sect".

> some interpretation of the Vedic texts, which doesn't actually entail all that much

If you studied the Vedas you would know why this issue exists in the first place. The Vedas talk of One Supreme Brahman who should be given Havis during a Yajna. The dispute between the sects is on who the Supreme Brahman is identified as. Every name in the Vedas is but a name of the Supreme. Vyasa composed the Brahma Sutras to unravel it. But then, as is the case with Dharmics, we have around 30+ commentaries on the Brahma Sutras itself. This, coupled with commentaries on Prasthanatrayi as well as interpretation of Puranas created sects.

All of them come within the umbrella term of Hinduism as all of it is Dharmic and native to the Indian subcontinent.