random/folder/path may refer to a directory called 'path', or it may refer to a file called 'path', either of which lives in 'folder'. It's ambiguous, and required a look at the contents of folder to determine whether 'path' is a file or sub-folder.
random/folder/path/ is unambiguously a directory.
This can give rise to unexpected results, unless you know what's going on.
For example:
mv myfile /archive/mystuff
what does that do?
It can do one of 2 things.
It can move 'myfile' into the 'mystuff' subdirectory ( **if it exists** ).
What if it doesn't exist? You mis-remembered the directory name, and it was actually 'MyStuff'. What happens then?
It sees there is no directory called 'mystuff', so it assumes you want to move 'myfile' into the '/archive' directory, and **re-name it as 'mystuff' along the way**.
Now you go looking for your archive of 'myfile', and it's not there!
Wail! The computer ate you file!
It's best to avoid the ambiguity by explicitly specifying the destination is a directory:
mv myfile /archive/mystuff/
That can only mean 1 thing.
And if the 'mystuff' directory does not exist, you will get an error.
It will not interpret it as a name-change of the file.
As an aside, your examples are 'relative path names', in that they don't start from root (/ ), they start from where you are right now, the Present Working Directory.
'/etc/hosts' for example, is an absolute pathname, because it gives the full path starting from root.
Again, you can use relative pathnames for simplicity, but absolute pathnames to avoid possible ambiguities.
