Problem:

Slow worms are considered lizards as opposed to snakes, both are reptiles. Now I get that there are traits that distinguish them (eye lids, ears ...). But snake species themselves vary already quite a lot.
The Wikipedia article on snakes states:
Based on comparative anatomy, there is consensus that snakes descended from lizards.

Required:

Question 1: How comes slow worms are considered lizards despite the loss of their limbs during evolution, whereas the same evidently has happened to snakes?

Question 2: What's the defining factor here? The time frame when it happened, that it happened independently (like the evolution of, say, an eye)?
Please describe the answers in detail.