Is a CD burner the same as external CD drive?

No, CD Drives and CD Burners are two different types of optical drives on personal computers that perform different functions regarding compact disk media.

CD Burners are optical drives can write data on a burnable disk. CDs are comprised of thin layers of dots computers use to burn information on. CD Burners are equipped with a special laser that burns binary code onto the CD's surface. CD Burners can both read and write CD disks.

CD Drives are not equipped with that special burning device, and have only a laser that can read the information stored on a disk. They can only read CD disks.