When we use mv command, what changes take place in HDD?

It's up to each filesystem how to handle a move within the filesystem (also known as renaming a file), but filesystems pretty much universally handle it by updating directory entries without moving the inode or file contents.

A move between filesystems (it doesn't matter if it's on the same physical medium or not) is handled as a file copy followed by a delete. This is in fact exactly what the mv command does. Obviously that means that the destination filesystem has to make a new copy of the file.