The shared task
Both approaches take input data and produce a prediction or decision that should hold for cases they were not trained on. This is the job description they have in common.
The same shape of problem
Consider three tasks. A spam filter maps an email to spam or not-spam. A price estimator maps a description of a house to a number. An image classifier maps a photo to a category. In each case the input is data and the output is a useful answer, and in each case the model must work on inputs it has never seen before.
Where the paths diverge
The two approaches agree on the destination and disagree on the route. One relies on a person to decide which properties of the input matter and to encode them explicitly. The other is handed the raw input and works out its own internal representation of what matters. Both routes end in a prediction; they differ in who does the deciding.
Why generalization matters
A model that only reproduces the answers it was trained on is useless. The point of learning from examples is to handle new ones, and this is true for both approaches.