When building an AI model, we have a model, training data and a training method. Traditional DL method emphasizes on the first two while using a relatively simple optimization method to minimize error (SGD). Meta-learning addresses learning efficiency and comes up with different approaches. For example, MAML develops a different optimization method to improve training efficiency.
Traditional DL or meta-learning tries to solve similar problems. The classification task actually has a broader sense than classes in DL. Each class classification can be viewed as a specific type of task.
Fewer samples force the researchers to come up with methods with better learning efficiency, rather than a more brute force approach. It is a goal that meta-learning wants to achieve since human is far efficient in learning than DL.