A meme is specifically a culturally transmissible unit of information. Duplicating culturally transmissible information is not necessarily the same thing as duplicating thoughts. For example, lots of people learn arithmetic but different people may think about how to do arithmetic in different ways.
Now it could be the case that one particular way of thinking about doing maths is better than another, i.e. - people can do maths faster with it or understand the results better. But if nobody puts time and effort into figuring out how to transmit that method culturally it won't be a meme. so there is a distinction between memes and thoughts. Moreover, when somebody figures out how to transmit an idea culturally he adds to its content and may substantially change it. So the meme version of the idea may be very different to what he was doing originally.
Another distinction between memes and ideas is that a person may think that he does not hold a particular meme when in fact he does. A parent may get annoyed with a child when the child disobeys the parent's instructions. The parent might then say "Do X because I said so." The parent may think that this is not his actual position, he has a very good reason he just can't explain it right now. But the parent is wrong. If he had some fabulous explanation and he wanted to tell the child he would do so. He literally does want the child to do X because he said so and not for any independent reason. Such ideas are not transmitted by people understanding their content, but by patterns of behaviour that help shield the content from being thought about and criticised.
For the best available discussion of memes, see "The Beginning of Infinity" by David Deutsch, chapters 15 and 16, which have detailed discussions of meme transmission and of similarities and differences between memes and genes.