Dumping Browsing History from inside a browser doesn't really "erase everywhere you've been" since the computer keeps some other records of processor use and error messages (most of which never get to the monitor) that make a fairly complete reconstruction of most of what you've done possible with the right magic boxes. It does get most of the trash out of the temp space to make the space useful for future browsing. Since it's done while the browser is running, any "live connections" can't be deleted, and it also seems more likely to zap cookies you'd like to keep.

With the browser shut down, Disk Cleanup gets a little more thorough cleanup of the useful temp spaces, since it can clean files that the browser might have had open, and for the most part in Win7 it leaves login cookies from sites you've "trusted" in your browser, or for ones that give you a "certified" (signed) cookie like (some) banks and such.

There's not a lot of difference, so you may find you like the other one instead of whichever one some other fool prefers.

Generally, in order to see cookies in Win7, you'll need to turn on "show everything" in Windows Explorer. Select C:\, Click Tools on the toolbar, go through "Folder Options" and turn on everything you can. (It's unlikely you'll want all that stuff to show all the time, so you might want to make notes so you can turn some of it back off later.)

IFF you're not frightened by command prompt, pretty much all temp files either have a .tmp filetype, or start with a ~ on the front end of the file name.

DIR ~*.* /S or DIR *.tmp /S will show most of them, although there may still be a few "protected ones" that remain hidden. If either of these shows only stuff you want to get rid of, just type DEL and hit F3 to fill in the rest of what you had to get the list, and it should delete everything it listed - except for the "protected" or open ones.

For some reason, a Command Prompt "ATTRIB" listing often shows lots of files that don't appear with a "DIR" listing, which is sometimes handy for poking around if you don't want to go full ADMIN. Kind of like knocking the dust off with a feather duster instead of getting out the pick and shovel to dig down deep.

John