The classification task in a multi-class classification problem has more than two mutually exclusive classes (classes that have no intersection or no attributes in common), whereas in a multi-label classification problem, each label has a different classification task, although the tasks are related in some way. For example, classifying a group of photographs of animals that could be cats, dogs, or bears is a multi-class classification problem that assumes each sample can be of only one type, implying that an image can be categorized as either a cat or a dog, but not both at the same time.
Now let us assume you wish to manipulate the image below.
The image above must be categorized as both a cat and a dog because it depicts both creatures. A set of labels is allocated to each sample in a multi-label classification issue, and the classes are not mutually exclusive. In a multi-label classification problem, a pattern can belong to one or more classes.