Taken directly from Vs Battles Wikia. Please give them all the credit for this.
Transformation is the ability to transform parts of one body or slightly modify their forms through external power-ups, gradual mutations over a period of time, or through limited or uncontrollable change in form.
Transformation is different from Shapeshifting. Whereas the former lies on said above, the latter is those who are able to transform the shape of their body to assume different identities, impersonate others, or modify the entirety of their body at will.