The traditional grammar of English was based on that of Latin since that was what early grammarians were familiar with, and possibly Aristotlean view that Latin was "closer to linguistic perfection" than English. Unfortunately, the direct application of Latin grammar to English doesn't work particularly well because of significant linguistic differences between Latin and English. Though both are Indo-European languages, English is a Germanic language whereas Latin was a Romance language.
Traditional grammar often influences pedagogic grammar. Scientific grammar often uses well-established traditional terminology, even though it's often inappropriate (e.g. present and past tenses ought to be called "close" and "distant" tenses, though in reality nobody uses those terms).
Teflpedia prefers modern scientific grammar, as that is more coherent, but mentions traditional terms where appropriate.