No, not usually — but sometimes yes and sometimes no. The two versions given by Cambridge for sit have the same vowel to our ears.
And sometimes one British-Isles speaker will use different sounds for the KIT vowel than another British-Isles speaker will, just as sometimes one North-American speaker will use different sounds for KIT than another North-American speaker will use.
None of that variation changes which abstract phoneme we mean by the KIT vowel. Every English vowel phoneme has zillions of different actual pronunciations each! Allophones don’t matter. If they did, nobody would ever understand when a New Zealander ordered “Fush-un-Chups”. :)
Examples Needed, Please
It really is impossible to know which words the asker is thinking of until he tells us, but one potential systemic difference I can think of is that many and probably most Americans today now use the tense FLEECE vowel not the lax KIT vowel before orthographic ‑ng and ‑r, so like in king and beer.
That’s because the tense–lax distinction is normally neutralized in those positions in American English. Because there are no minimal pairs for words like king and beer between tense and lax versions, it does not matter and so gets neutralized without anybody noticing.
It’s not all black and white, and I may be unintentionally exaggerating that particular difference here.
Phonemes ≠ Phones
If you look at the ɪ row from the Wikipedia chart of “diaphonemes” here, you’ll see that the KIT phoneme has many, many, many different pronunciations everywhere. This is just as true for this phoneme as it is for the others. Vowels have no single pronunciation. Here’s that row laid on its side to read it better as a column:
Dialect |
Pronunciation |
African American Vernacular English |
ɪ~iə̯ |
Boston English |
ɪ~ɪ̞~ɪ̈ |
Cajun English |
ɪ |
Californian English |
ɪ̞ |
General American |
ɪ~ɪ̈ |
Younger Southern American English |
ɪ~ɪjə~iə̯ |
Australian English |
ɪ~i |
Brummie |
ɪ~i |
Estuary English |
ɪ~ɪ̈ |
Northern England |
ɪ |
Contemporary RP |
ɪ̞ |
Belfast Ulster Irish English |
ɪ̈~ë |
Traditional Ulster Irish English |
ə~ɘ |
Ulster Scots |
ɛ |
Dublin Irish English |
ɪ |
Cultimate New Zealand English |
ɪ̈ |
Broad/General New Zealand English |
ə |
Scottish English |
ɪ~ë̞~ə~ʌ |
Cultivated South African English |
ɪ |
General South African English |
ɪ̈, ɪ |
Broad South African English |
ɪ̈, i |
Abercraf Welsh English |
ɪ |
Cardiff Welsh English |
ɪ̞ |
This is just like for all the other vowel phonemes in English. Nobody ever says anything the same in one place as anybody else does in another place. These varying pronunciations of KIT are all allophones that you need to learn to stop hearing. They are not different phonemes, only different sounds. Mishearing different sounds as somehow representing different phonemes is a common mistake by learners of English. The sounds don’t matter, believe it or not.
Furthermore, these values only count for the stressed KIT vowel when it is surrounded by unvoiced stops. When you use a voiced stop like b, d, g to either side, or a nasal like m, n, or a velar like k, g, or a resonant like r, l, then any of these factors can again completely change the actual sounds used to pronounce this phoneme.
Phonemes are not what you hear; they're only what you think. Phones are what you hear and say, and every vowel phoneme in English has more allophones than you can shake a stick at.
Your task is to be able to unhear these minute difference in the sounds all these different allophones make in different regions, speakers, and phonological environments.