What's the difference between access to moderator tool(which requires 10000 rep point) and being an moderator(official moderator)?
A 10k user has access to a number of tools that really just assist with the utility of their normal privileges - access to close vote lists, access to deleted questions, overviews of general problem areas, and vision to the cookie-cutter flags like "not-an-answer". You can see a general overview of these privileges at this Meta Stack Overflow post.
A moderator with a diamond has all the privileges of all reputation levels (regardless of their own reputation), as well as a number of additional capabilities to assist on a much greater degree of management. These include that their close/delete votes are binding (one vote will always settle the action rather than requiring 5), they can lock and protect posts, and they can suspend problem users. You can read up a description of all of the diamond powers at this other Meta Stack Overflow post.
I'd say check out
to compare and contrast.