Does an ear discharge mean my baby has an ear infection?

No, could be wax. Not all ear discharge is considered abnormal. Ear wax may drain out of the ear canal and is generally not associated with any pain or discomfort. In a child who has been sick with a cold and severe ear pain, ear drainage could be due to a ruptured ear drum from a middle ear infection. Also if your child has ear tubes, infected drainage may be due to an ear infection as well.
Possibly -maybe wax? Ear drainage, especially if it is pus-like, may be a sign of an ear infection, but parents can easily mistake draining ear wax for pus. Even if your baby isn't fussy, it'd be a good idea to have the doc check.
Usually. Most episodes of true ear discharge (pus or blood) represent an infection of the middle ear, commonly referred to as an ear infection. The discharge is coming from either a ruptured ear drum or a surgically placed ear tube. Ear discharge may also represent what is commonly called a "swimmer's ear, " or inflammation of the ear canal, which can be caused by cotton swabs, water or a foreign object.