How do you define functional testing with two popular and seemingly contradictory explanations?

I've been researching the definition of functional testing and can't come across a concrete explanation and would appreciate some additional info to help reconcile this.

The two main ideas I have come across are:

1. Functional Testing as a Testing Type and is comprised of the following Testing Levels: Unit Testing, Integration Testing, System Testing and Acceptance Testing.

2. Functional Testing as a separate level from Unit Testing and Integration Testing (sometimes a subset of System Testing other times precedes it) that tests the product end-to-end with a Black-box approach. Purpose is to verify all functional specifications defined.