They mean the same. "Iron out a problem" is not very common, in my experience. "Iron out differences (between people)" is common.

Hey Daniel, how are you? I hope you are doing just fine! In this case, I would advise you to use a simple statement like ''I will do my best to solve this problem''. However, both ''sort out'' and ''iron out'' can be used to convey the same meaning, which is ''to resolve a problem''. Regardless of the meaning, you should know that the very concept of each phrasal verb is what differs them. 1) Literally, the idiom ''iron out'' means ''to remove wrinkles from something, especially a piece of fabric, using a flatiron''; whereas figuratively it gets the meaning of ''to ease a problem; to smooth out a problem''. (Here ''problem'' is synonymous with ''wrinkle''). This expression uses ironing wrinkled fabric as a metaphor for smoothing differences. E.g.: ''They managed to iron out all the problems with the new production process''. E.g.: ''Our parents finally ironed out their differences'' 2) Literally, the idiom ''sort out'' means ''to arrange according to class or category'' (e.g.: ''Let's sort these cards out'' or ''Would you please sort out your socks?''). However, when used figuratively, it conveys another meaning, which is ''to study a problem and figure it out''. E.g.: ''The couple almost broke up, but they managed to sort things out!''. E.g.: ''What should I do? I can't seem to sort out this math problem.'' Hope that helps!!! :)

There basically the same but "sort out this problem" is used much more but you can use them the same way and it wont matter. Hope this helped