1. What are some terms that relate to this phenomenon? I want to beware of similar cases.
2. What are the reasons?
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I merely replicate Janus Bahs Jacquet's comment above:
It's not a suffix in either word. The base verbs are lege and nege, the former from Old French (ultimately from Latin litigāre), the latter straight from Latin nēgāre. They're completely unrelated to each other, and the fact that they happen to contain the same three letters in their English form is just happenstance.