What are some of the different types of tooling?
While many tool manufacturers have more extensive answers to this, which you can seek out, here are the basics:
Endmill – used for removing material in a horizontal path, generally has a flat tip

Drill- used for drilling round holes
Ball mill – same as the endmill, but has a round tip. This tool isn't a good choice for making square corners.

Chamfer tool – endmill shaped with an angled tip

Keyway/dovetail – used to create undercuts

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All images from Harvey Tool Company, LLC.