What is the difference between the two words: "ibn" and "bin"?

The difference between affirming the alif of 'wasl' in the word "ibn" and omitting it is only in the orthography, where the alif is omitted if the word functions as an adjective between two proper nouns, the second of which is the father of the first, such as: "Ali ibn Abi Talib." However, if it does not come between two proper nouns, the second of which is the father of the first, then the alif is affirmed in both writing and pronunciation, such as: "Ibn Umar."