Are they generally pronounced with the same vowel, or not?
Yes, red and read (past tense) typically have the exact same vowel phoneme (which we can write "/ɛ/") and are homophones. This exact phonetic pronunciation of this vowel phoneme /ɛ/ may vary between speakers, or even from time to time with the same speaker. For example, some accents of English use a variant that is phonetically a closer/higher vowel [e], and some accents use a more backed variant, [ɜ] or [ɐ], as a pronunciation of this same vowel phoneme (the vowel found in words like dress).
But it would be surprising if a speaker consistently used a noticeably different phonetic vowel for red and read, and I would expect that to occur only in a non-native accent that was influenced by the different spelling of the words. (There also apparently may be some alternative forms of the words of the words in British dialects, but I think those would rarely be encountered outside of the certain specific contexts.)