Chace ¡°anyway¡± is used when we want to change the subject completely, or when we want to bring back the original subject after being interrupted. For example:
A: ¡¦so that¡¯s why I didn¡¯t like that movie.
B: Oh I see. I won¡¯t go see it then. Anyway, where do you think we should have dinner tonight?
A: I really don¡¯t think this is a good time to¡¦
B: Excuse me. Could you tell me where the bathroom is?
A: It¡¯s at the end of the hall. Anyway, as I was saying, I don¡¯t think this is a good time to invest in gold.
The expression ¡°by the way¡± is used when we suddenly remember something that we want to say to someone. For example:
I¡¯m going to the supermarket after work today. Oh, by the way, Harry wants to know if you¡¯re coming over for dinner this weekend.
I watched a really good show on TV last night. Oh, by the way, here¡¯s the DVD you lent me last month. Thanks for letting me borrow it.