All vampires can turn into a bat and fog, but a shapeshifter can turn into breathers and even other vampires.
A shapeshifter is, according to Bertrand, actually a type of vampire. They can render themselves invisible (even being in the same room as powerful vampires without the latter noticing) and can morph into both humans and vampires. Bertrand said that morphing into breathers and other vampires "can only be done by using forbidden, dark forces" and requires centuries of studying. He also said that dark magic warps the mind.
Shapeshifters can also twist their own bodies into impossible shapes. This is shown in "Kiss of Death" when Elizabetta opens her mouth unnaturally wide, avoids being zoned, and extends her arms to an extrordinary length towards Malik.