MYSQLI_ can only access mySQL databases,
PDO can access mySQL databases as well as other databases (but because it supports multiple databases it is slightly slower).
Both support PREPARE and BIND commands which allow you to keep your SQL and data completely separate and so remove all possibility of injection.
MYSQL_ is being removed because it doesn't support all the modern functionality that mySQL databases support such as PREPARE and BIND.
It is just the MYSQL_ interface that is being deleted. The other two ways to access mySQL databases still exist and both have been recommended as replacements for MYSQL_ since PHP 5 was first released.