A different bet
A rule-based system begins with instructions written by people. A learning system begins with examples.
Imagine sorting email. With rules, a person might list suspicious words, addresses, and links. With learning, people show the machine many messages already labelled "spam" or "not spam." The machine adjusts itself until it becomes better at telling them apart.
The machine still follows a program. The difference is that people do not have to write every decision rule themselves.
That was the new bet: instead of describing every pattern in advance, let the machine find useful patterns in examples.