Block devices are also associated with a device node, which also has major and minor numbers.
Although character and block devices are identified using major and minor numbers, they are in different namespaces. A character driver with a major number 4 is in no way related to a block driver with a major number 4.
With block devices, the major number is used to identify the device driver and the minor number is used to identify the partition. Let's look at the MMC driver on the BeagleBone Black as an example:
# ls -l /dev/mmcblk*
brw-rw---- 1 root disk 179, 0 Jan 1 2000 /dev/mmcblk0
brw-rw---- 1 root disk 179, 1 Jan 1 2000 /dev/mmcblk0p1
brw-rw---- 1 root disk 179, 2 Jan 1 2000 /dev/mmcblk0p2
brw-rw---- 1 root disk 179, 8 Jan 1 2000 /dev/mmcblk1
brw-rw---- 1 root disk 179, 16 Jan 1 2000 /dev/mmcblk1boot0
brw-rw---- 1 root disk 179, 24 Jan 1 2000 /dev/mmcblk1boot1...