In my world, we use the terms as follows:
functional testing: This is a verification activity; did we build a correctly working product? Does the software meet the business requirements?
For this type of testing we have test cases that cover all the possible scenarios we can think of, even if that scenario is unlikely to exist "in the real world". When doing this type of testing, we aim for maximum code coverage. We use any test environment we can grab at the time, it doesn't have to be "production" caliber, so long as it's usable.
acceptance testing: This is a validation activity; did we build the right thing? Is this what the customer really needs?
This is usually done in cooperation with the customer, or by an internal customer proxy (product owner). For this type of testing we use test cases that cover the typical scenarios under which we expect the software to be used. This test must be conducted in a "production-like" environment, on hardware that is the same as, or close to, what a customer will use. This is when we test our "ilities":
Reliability, Availability: Validated via a stress test.
Scalability: Validated via a load test.
Usability: Validated via an inspection and demonstration to the customer. Is the UI configured to their liking? Did we put the customer branding in all the right places? Do we have all the fields/screens they asked for?
Security (aka, Securability, just to fit in): Validated via demonstration. Sometimes a customer will hire an outside firm to do a security audit and/or intrusion testing.
Maintainability: Validated via demonstration of how we will deliver software updates/patches.
Configurability: Validated via demonstration of how the customer can modify the system to suit their needs.
This is by no means standard, and I don't think there is a "standard" definition, as the conflicting answers here demonstrate. The most important thing for your organization is that you define these terms precisely, and stick to them.
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