The answer is either yes or no - it depends just how 'proper' you want to be. In ultra-correct Received Pronunciation they are actually different sounds. When I first studied English phonology, many years ago, the word 'pour' was an example of the /ʊə/ diphthong, made up of an 'oo' followed by an 'uh', making a sound which rhymed with 'fewer'. Pour /pʊə/ Tour /tʊə/ but Pore /pɔː/ Tore /tɔː/ However, language changes, and even RP has become more relaxed. Few speakers of standard English in England now make this distinction. The Oxford dictionary now lists the pronunciation of both 'pore' and 'pour' as /pɔː/, but gives two alternative pronunciations for 'tour' : the traditional /tʊə/ and the more relaxed /tɔː/ - the same as 'tore'. The original difference still persists in some regions, such as Scotland, for example. I was also interested to see that Australian English also retains this distinction, according to Jmat's comment. I also read an article recently comparing the speech of the Queen and her grandson Prince William. While the Queen still uses the traditional /ʊə/ sound in words such as 'pour', William uses the more relaxed and modern /ɔː/. By the way, the only difference between British and American English regarding these words is the pronunciation of the 'r'. The vowel sound is the same. GB English: /pɔː/ US English /pɔːr/

I agree with Susan and Paul about "pore” and "pour" sounding the same, but I would pronounce "tore" and "tour" very differently! It must be a regional thing. I pronounce "tour" so it rhymes with "pure", "fewer" and "cure". I pronounce "tore" so it rhymes with "more", "door" and "sure".

not to mention paw and pore; tore and tour are a different kettle of fish however 哈哈

Yes, I have lived in many places in the US and just about every place pronounces tour and tore plus pour and poor exactly the same in proper English. Some individuals thrive on their own speech and may stretch-out certain words such as in rural south, but the correct way is to pronounce them the same.

I'm not sure exactly what you're asking. In the UK we pronounce 'poor' and 'pour' the same. In the US they also pronounce the words the same way. The same thing applies for 'tore' and 'tour'. I think this is what you wanted to know. Your question is a bit confusing because as native speakers we generally don't distinguish American vs British English. Its just English. Now English can be spoken with different accents but its still the same language underneath. But the way we pronounce 'r' is slightly different between the UK and the US. It makes no difference to whether we understand the word or not, its just a slightly different pronunciation. But whatever way you choose you pronounce them the same way.