What do you mean by delete? Talking about the NTFS disk format below btw.
As in, physically isn't there, or just regions on disk which are marked for reallocation?
The difference is, in the second scenario, the files MAY be recovered, depending on how fragmented your HDD is, and the level of HDD output activity there is. Generally the OS writes 10 times per a second. When you 'delete' a file, you're actually just marking it's owned segments to a reallocatable state. The segments are not actually touched until another file needs that space.
The first scenario is similar to the second, except when a file is 'deleted' it's segments are zero'd right after the they're marked for reallocation. Making them unrecoverable.
I ask this because if you've been doing something illegal, you should go with the first method of deletion(though it takes a lot longer depending on file size).