Full Backups include all data within the backup scope. For
example, a full database backup will include all data in the
database, regardless of when it was last created or
modified. Similarly, a full partial backup will include the
entire contents of every file and filegroup within the scope
of that partial backup. 

Differential Backups include only that portion of the data
that has changed since the last full backup. For example, if
you perform a full database backup on Monday morning and
then perform a differential database backup on Monday
evening, the differential backup will be a much smaller file
(that takes much less time to create) that includes only the
data changed during the day on Monday.

Full backup
Differntail backup
Transcation log backup
File & Filegroup backup

Full backup : it's take full database
differential backup : what are the changes made after 
fullbackup to current backup is called differntial backup

the types of backup are 
full database backup
differential database backup
transactional log backup
file and filegroup backup
the difference between full and differential backup is in 
full backup it takes backup for entire database including 
transactional log files. but in diffrential database backup 
it take only the changes happened between full database 
backup and current backup.