/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!
The only examples I can find after searching are proper nouns: The city of Quincy (/ˈkwɪnzi/ KWIN-zee) as mentioned in comments, and the highest mountain in Australia Mount Kosciuszko (/ˌkɒziˈʌskoʊ/).
Standard (i.e. RP or GA) pronunciations of sacrifice and discern now use /s/.
Best Answer
In both American and British English, there is an emphasis on the first O, but not too much. For example, "astronomy" is pronounced:
However, in Indian English, I have heard many people pronouncing it astrOHnomy, basically giving the O in "astro" the same emphasis as the O in "micro" and tacking on the "nomy" (rhymes with "mommy"). This is completely different from the pronunciation above, and is wrong in American/British English.