When you mount something, you mount a filesystem: Basically, a particular way to assign a number of disk blocks to some file name. A filesystem usually occupies one partition, and there may be several partitions on a harddisk.
Unix-centric filesystems (like
ext4) implement the concept that every file "belongs" to a particular user (uid
) or particular group (gid`).
Other filesystems (FAT, NTFS) may not implement this concept, or may have other ideas what constitutes a "user". In this case, Linux sometimes tries to map the "foreign" ownership and permissions to Linux ones, and sometimes it just assigns a particular user and group to all files.
You can't just change ownership of all files of an ext-filesystem to a particular user using mount options. You can apply
chgrp to it, but in many cases this may not be a good idea, in particular for a filesystem that contains your Linux system files and programs.
Therefore, don't do that. Instead, make sure your own files are created with you yourself as owner. Create new groups and add yourself to the groups if necessary. In short, just do some sane administration. "All files should be mine" doesn't work.
If you want to mount a "foreign" filesystem, you can, depending on the filesystem, supply the
gid mount options. See
man mount for details.
This works fine for reading, and for writing FAT-based filesystems, but I wouldn't recommend it for writing stuff to NTFS-based filesystems.
It's not important if the disk is internal or external. In fact, the disk isn't important at all, the type of the filesystem is. You didn't say which types of filesystem you have, or even which partitions you want to use.
The only thing one can see from the information you gave is that one of them is NTFS (the "2 TB" one, not the "8 TB"), which doesn't mix well with Linux in the first place.
You get downvotes because it shows that you haven't understood basics about Linux, and are about to do things that will bite you in the long run. Don't do those things.