An R in a circle after a name means registered trademark, whereas TM means trademark but not registered. I've never seen trademarks (registered or otherwise) after the initials IGCSE though. I'm afraid I can't answer your question as I'm a little confused by it.
so basically this label doesn't matter so much right? example is the document i uploaded which is 2020 exam (according to Cambridge IGCSE official website there is a change of format of the papers recently if i didn't make it wrong, so the label is waiting to become an R mark?)
and my question is no matter which exam board you are using CIE, or CAIE, the content just sticks to the syllabus so there is no difference between difficulty levels or requirements etc. right? If there are some differences what are they?
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.
If it has past papers though, past papers are fine for revision. You can't really go wrong with past papers.