I think they pretty much carry the same meaning and can be used interchangeably in writing except that 著名 feels slightly more emphatic and sounds more sophisticated than 有名.

no....

They are different. 1.Meaning is different.The 著名 originaly indicates that note the writter‘s name in his /her works,and its extend meaning is that someone is very acomplished in some fields,while the word 有名 only means very famous. 2.grammatical function is different.著名 can be used attributively,for example:她是一位著名歌唱家；有名 and 著名 all can be act as complement,for example:她唱歌很有名/ 她在这个领域很著名.

著名正式些，比有名的程度更深 有名相对著名更口语化些

著名比有名更有名，就像是“最喜欢”、“比较喜欢”和“喜欢”一样的道理