Postdoc application asks for both cover letter and research statement, can they overlap? Most postdocs I have applied for wanted a cover letter (including research interests) and a CV.

I have now come across one that wants both a cover letter and a one page research statement.

The cover letter should be a very short document just stating my interest in the position and what is included, while the research statement should go over what research I have done an my interest in the project, right?
Yes, you have it right. Just be very careful not to repeat yourself in either of the documents. 

The reason they're asking is because they feel they are different enough documents that they should be completely separate, and you should probably treat them the same (in this case).