A weak verb isn't quite the same thing as a regular verb. Oxford defines a weak verb as follows:
Grammar Denoting a class of verbs in Germanic languages that form the past tense and past participle by addition of a suffix (in English, typically -ed).
As implied by "typically", a weak verb doesn't necessarily end "-ed". Verbs that ends -ed or -t in their past tense (and don't change their vowel¹) are weak (e.g. "spilt" is a weak past tense of "spill") - but only verbs that end -ed in both their past tense and their past participle are regular. Oxford defines "regular" as "following the normal pattern of inflection" - and that's "-ed" in English.
[¹As noted later, a change of vowel does not necessarily make a verb strong, from a technical point of view.]
Strong verbs are all considered irregular in modern English, but the reverse isn't true. Just as not all weak verbs are regular (but all regular verbs are weak), not all irregular verbs are strong.
According to "Hybrid Inflection in Middle and Early Modern English" by David Fertig of the University of Buffalo (PDF), "tell" is technically a weak irregular, having begun life as a weak verb but developed a vowel alternation.
Strong/weak is an interesting distinction, especially from the point of view of historical and comparative linguistics. But for learners, regular/irregular is a more useful and clear-cut distinction in practice.
Some other verbs that exhibit features of both strong and weak verbs include most of the modals. These are known in grammars of Old English as "preterite-present" verbs, because the infinitives of "can" and "will" had a different vowel (modals have no infinitives in modern English and are cited by their finite forms instead) - "can" exhibits a vowel shift (the old infinitive was "cunnan" in OE) typical of strong verbs in their preterite (simple past), whilst "could" retains the original vowel but adds a dental suffix, as expected of a weak verb. Yet "can" is present tense, hence the term "preterite-present".
