In those examples, like /ʃəʊ/ and /ʃoʊ/, the correct answer is nothing.

If you look at the pronunciation guides from your favorite dictionary, say Cambridge or OxfordLD or Dictionary.com, they only describe /əʊ/ and /oʊ/ as single units, representing the vowel in words like "goat." They also use /ʊ/ on its own to represent the vowel in words like "put." But the "ʊ" in /oʊ/ has no independent meaning of its own.

So why do they use two letters to represent a single vowel? The answer is that most speakers, in most contexts, pronounce /oʊ/ as a diphthong. The use of the symbol "ʊ" to represent the second half of that diphthong is arguably misleading; I'll leave it to Geoff Lindsey to explain why it might be preferable for dictionaries to use /ow/ to represent that diphthong instead (with /ow/ again, though, interpreted as a single unit).

But one question remains: why do some dictionaries use different symbols, /əʊ/ and /oʊ/, when describing pronunciations in British and American English, respectively? This is going to take some work to explain, because you'll need to understand the difference between phonemes (word parts) and phones (mouth noises).

I'm going to give an extremely oversimplified explanation of how this distinction leads to confusion. IPA symbols like "ə" and "ʊ" are typically used in one of two ways. First, they can be used to objectively describe the sounds of which a person's speech consists at various levels of detail. Used this way, to represent phones, the IPA symbols correspond to the sounds described on the IPA chart; you can see versions of this chart with corresponding audio recordings online, e.g. here. IPA symbols used to represent phones (in phonetic transcriptions) are generally placed between square brackets. But dictionaries do not use IPA symbols this way. After all, the exact pronunciation of the vowel in "goat" differs between speakers, and this same vowel can be pronounced in different ways in different environments, so objective descriptions of mouth noises would be very complex and of little value. Instead, dictionaries use IPA symbols to represent phonemes, more abstract units of sound used to convey meaning (see Wiki). When IPA symbols are used to represent phonemes (in phonemic transcriptions, which are usually placed between slashes rather than square brackets), they do not correspond in any direct way to sounds on the IPA chart. That said, the IPA symbols chosen (by e.g. dictionaries) to represent phonemes aren't entirely arbitrary either. They're supposed to correspond (very, very loosely) to the phones typically used when pronouncing them. But again: this correspondence is not at all precise, so recordings of the phones [o] and [ʊ] on the IPA chart are not directly relevant to the interpretation of the phoneme /oʊ/ in a dictionary's transcription.

Now, in American English and British English, the vowel phoneme in "goat" is pronounced differently. In particular, the start of that diphthong in American English is often close-ish to the phone [o], whereas in British English it's often closer to [ə]. Since the phonemic transcriptions used by dictionaries are supposed to correspond at least loosely to the phones used in actual speech, some dictionaries use different symbols, /əʊ/ and /oʊ/, when representing that phoneme in British and American English, respectively, though this is often more a matter of convention than phonetic accuracy. Note that other dictionaries don't do this; OxfordLD, for instance, uses /əʊ/ in phonemic transcriptions for both dialects: again this is because dictionary transcriptions need not correspond precisely to actual sounds. (As stated above, in phonemic transcriptions it might be wiser for them to use /əw/ or /ow/ instead.)

But again: this is only a loose correspondence. If you read the very precise phonetic transcriptions of the word , you can see how the phones used by actual speakers to pronounce the start of that diphthong vary widely. In their recording of British Received Pronunciation, it's [ə]; in "Standard Canadian" it's [o]; in "Standard US" it's [ʌ̈], in the traditional Boston accent it's [ɔ̈], et cetera. These phones actually do correspond to the values on the IPA chart you can find online.