Hi Ruby Your question is very interesting. As FireflyTech says, there is a difference, but in the context that you are asking (battery compartment cover/lid), it is not easy to explain which to use. Yes, in general, a cover could be considered larger than a lid, but not always. Also, lid is usually only used when it is a cover on the top of something. Also, a lid can only ever cover a hole in something while a cover can cover a hole and cover the whole object as well. To make things even more difficult, there are some occasions when only one or the other is correct. For instance, a teapot has a lid; a box has a lid; a dustbin has a lid; a drain can have a lid or a cover, but a manhole only has a cover! I think that it is probably safer to use 'cover' unless you are certain that 'lid' is correct.

of course there is a difference. first Lid is a noun and cover is a noun and a verb. also it depends on how it is used. for example: as a noun the cover of a book ( you can't say the lid of a book) also the cover of a magazine "don't judge a book by its cover" (you can't say "don't judge a book by it's lid") as a verb : cover him up (you can't say lid him up) or the old english slang "Put a lid on it" means to be quiet

there is absolutely no difference

sure, there is a difference as in US food code "A cover or lid for EQUIPMENT" a cover refers to hide the equipment and the word "lid" refers to top or cover of a container

No diffrence !