/i:/ is the vowel that we find in the word FLEECE. I put that word in capitals because that is how that vowel is often referred to by linguists: the fleece vowel - or FLEECE for short. (This is not random, the word was specifically chosen for a number of specific reasons.) It is the vowel sound at the end of the word guarantee. In transcriptions of British English it has a colon [ : ] in the symbol to describe the length.
/ɪ/ is the vowel in the word KIT. It is known as the kit vowel - or KIT for short. It is the vowel we find in prefixes and suffixes, the bits we stick onto the beginnings and ends of words. So, for example it is the vowel we hear in --ing verb endings.
The vowel represented by /i/ at the ends of words in dictionaries is usually referred to as the happy vowel - HAPPY. This vowel may sound like either FLEECE or KIT, but is always short in duration.
If you say the < y > sound that we find in the word yes, and then say the < e> we find in the word end, the kit vowel is somewhere between the two sounds. This is the first vowel in the word infinitely. This word would sound very odd to a native speaker if it was said with a fleece vowel, /i:/! It would sound like a made-up word: eenfinitely.
The Original Poster asks if there is a big difference between these vowels. If we are talking about the physical difference between the sounds, the answer is: no. In fact, it is very unusual to have two vowels that are so similar in one language. They are very close together. In most languages these would count as one vowel. However, if we are talking about the meaning, or the effect on a listener, the answer is: yes! There is a big difference. There are very, very, very many words that we can be confused about if you say the wrong vowel. For example, the words peace and piss. Nobody wants to say Piss man!, when they mean Peace man!.
If you want to type IPA script, this website is very useful
Hope this helps,
Peace!
North America has what we call the father-bother merger, where /ɑ/ and /ɒ/ often end up as the same sound, oftentimes /ɑ/.
So thus /ɑ/ would be a better choice in North America.
Merriam-Webster's system is a bit unique. I don't like to use it in a linguistic discussion. /ä/ = IPA /ɑ/.
IPA is the more universal option for phonetics as a science, even though several symbols will trick English speakers (e.g. /a/, /e/, /o/, /y/ don't exist alone in major English dialects, and /j/ is not the English J, it is the Y consonant, and people love to eschew the standard rhotic sign in English for the trill symbol /r/, which does not exist in most English speech).
Across the pond, Received Pronunciation British and other dialects don't merge "father" and "bother" vowels like that, thus you get /ɒ/ to accommodate (by the way, /ɒ/ is the rounded version of /ɑ/.) Which transcription is "correct" would depend on the dialect of focus, in this case American English.
Best Answer
The general rule you're looking for is that the vowels in stressed syllables are pronounced as you'd expect (in this case /ʌ/), and vowels in unstressed syllables are pronounced reduced. About 90% of vowels reduce to a schwa when unstressed.