Do files/directories belong to a user AND a group?

I'm trying to understand how file permissions work in Ubuntu. However, I can't understand the difference between user and group permissions.

In here it says:

Owner permissions − The owner's permissions determine what actions the owner of the file can perform on the file.

But it also says:

Group permissions − The group's permissions determine what actions a user, who is a member of the group that a file belongs to, can perform on the file.

So does a file belong to a user or a group? If the 2nd column shows the group permissions, how can those permissions be any different from the user ones?

as mentioned above there are 3 sections to the permissions for an example which may be easier to understand here is how it is broken down

say root is the owner/user of the file say video is the group and then as mentioned there is the world/other section which covers anyone that doesn't fit in the first two.

Now if the file has permissions like

Read/Write for root

Read for the group video with user1 as a member of that group

and none for world/other

Then the root user would have full read write control over the file. Any user in the video group (user1) would have read permissions but would not have access to modify the file. Anyone else would not even be able to view the contents of the file.

as mentioned sudo chmod can be used to change the permissions of a file. Usage of chmod is too large to explain here but a simple breakdown is like this:

u is for user,
g is for group,
and o is for others.

r is for read permission,
w is for write permission,
x is for execute permission.

so if you wanted to set a file so that the user/owner of the file can have full access and you wanted the group to have read and be able to execute the file (such as a script) and you wanted everyone else only be able to execute the file the command would be:

sudo chmod u+rwx, g+rx, o+x /path/filename

to remove a permission you just use a minus instead of the plus... so if you decided that you didn't want "world/other" to be able to execute that file you would just use

sudo chmod o-x /path/filename

You will also see numbers used at times and I would actually have to look those up but basically I know that 7 is full permissions so if you did:

sudo chmod 777 /path/filename 

it would set the permissions to read write execute for user (first seven) group (second 7) and world/other (third 7).

There is also a recursive code (-R note the capitalization it must be uppercase) .. if you wanted to change all the files in one directory and its sub-directories (be careful with this command because if you type the wrong path you can set permissions for files you may not want to touch) but it would look something like this:

sudo chmod -R 777 /home/user/blah  

this would change the permissions for the folder blah, all the files and all its sub-directories and files to have full read/write/execute for anyone.

Hope this gives you a better understanding of chmod and permissions. If you need more you can just do a search on chmod commands and you should find the information you need