A: It depends on how much of a purist you are and how literal you want to be. We think of it this way: In literal terms, a converter is designed to either turn an analog signal into a digital signal or vice-versa (or to do both). It probably doesn’t have direct connectivity for hooking up to your computer — an intermediary card or other device is required to connect it to the computer.
An audio interface, on the other hand, serves as a complete go-between for the computer and your audio signals in the analog and digital domains, and as the hub for your computer-based studio. It almost certainly has converters built in, but it also has a connection for hooking straight up to the computer (e.g., Firewire or USB). An interface usually also has other features such as onboard mic and instrument preamps, headphone outs, monitor outs and volume control, and a number of connection types for various signal formats. It may also have a built-in MIDI in and out.
Confusion can sometimes arise because these days, the defining lines are blurry. Many devices we would traditionally think of as “converters” have, for example, a built-in USB connection for hooking up to your computer. This can allow them to serve as rudimentary interfaces. However, they tend to not include all of the features and capabilities we discussed above.
So, is a D/A converter with a USB port, a headphone jack, and monitor outputs with a volume control an interface? This question brings us full circle back to the beginning of our discussion: the answer depends on how literal you want to be in your definitions.