Q:

Suppose you have permission to write to a file but not to delete it - What rights do we talk about?

Suppose you have permission to write to a file but not to delete it.
What rights do we talk about?
Read and write rights?

A:

To write to an existing file you need write permissions for that file. 
To delete a file you need write permission for the folder that contains that file.

A:

Florian's answer is not quite complete on my system: I need both write and execute permission on the directory in order to delete a file in it.
Sample session:
I'm running a well-seasoned Debian with the ext4 file system. I create a directory with a file in it and then change the directory and file permissions before I try to delete the file. 
File system ext4:
testuser@www:~$ df -T .
Filesystem     Type 1K-blocks     Used Available Use% Mounted on
/dev/sda3      ext4 152326340 44429904 100196624  31% /

Let's create a directory and a file in it:
testuser@www:~$ mkdir d
testuser@www:~$ ls -ld d
drwxr-xr-x 2 testuser testuser 4096 May 21 16:19 d
testuser@www:~$ echo kjhkjh > d/f
testuser@www:~$ ls -l d/f
-rw-r--r-- 1 testuser testuser 7 May 21 16:19 d/f

Expected: Cannot change file catalog without write permission on it:
testuser@www:~$ chmod 100 d && ls -ld d
d--x------ 2 testuser testuser 4096 May 21 16:19 d
testuser@www:~$ rm d/f
rm: cannot remove 'd/f': Permission denied

Unexpected: Cannot change file catalog without execute permission on it:
testuser@www:~$ chmod 200 d && ls -ld d
d-w------- 2 testuser testuser 4096 May 21 16:19 d
testuser@www:~$ rm d/f
rm: cannot remove 'd/f': Permission denied

I need both write and execute permission on it:
testuser@www:~$ chmod 300 d && ls -ld d
d-wx------ 2 testuser testuser 4096 May 21 16:19 d
testuser@www:~$ rm d/f

As an aside: When the file (but not the directory) is write protected rm asks for permission before deleting. After all, deleting a file can be considered an extreme form of writing to it. There is no difference in lost data between echo -n "" > d/f  and rm d/f in the common case that there is no other hardlink to the file.
testuser@www:~$ !echo
echo kjhkjh > d/f
testuser@www:~$ chmod 700 d && ls -ld d
drwx------ 2 testuser testuser 4096 May 21 16:21 d
testuser@www:~$ chmod 000 d/f && ls -l d/f
---------- 1 testuser testuser 7 May 21 16:21 d/f
testuser@www:~$ rm d/f
rm: remove write-protected regular file 'd/f'? y
testuser@www:~$  ls -l d
total 0
testuser@www:~$

