CIE and CAIE is the same company - both Cambridge. They are just abbreviations for the same exam board.
It looks as though they've registered some of their abbreviated monikers, and not registered others. It makes no difference, it's all the same.
The difference in syllabus would be if you were to look at an IGCSE by Pearson Edexcel as that's a completely different exam board so their papers would have a different syllabus to anything by Cambridge.
Sometimes exam boards do bring out new syllabuses and get rid of their old ones, for example Cambridge is bringing out a new IGCSE Computer Science syllabus from summer 2023, so the last chance to sit the old syllabus is autumn 2022.