[glial]

Typically the two systems are called 'model-free' and 'model-based' learning.

Model free (system 1) is fast, stimulus-response mappings. In ML, these mappings are called a policy. Most of reinforcement learning, including deep-learning-based RL, is model free.

Model-based (system 2) is less widely used. In this case, an agent or system is trying to learn the dynamics of a system and use those to project or forecast into the future. This is really helpful for e.g. learning a control system. Being able to use a model of the world to make accurate predictions lets you plan.