An audio interface is more for production. A DAC/AMP is more for consumption. An audio interface generally (always?) has a DAC/AMP in it.
An audio interface allows you to do things like plug in a midi device, guitar, microphone etc. and get low latency input. So when you press a key on a keyboard or strum on the guitar you hear the sound in your headphones with little/no lag. Preferably on studio quality monitors or headphones (I use DT990 250ohm headphones for mastering these days). A DAC does none of these things. A DAC/external sound card just takes output from a computer (generally over USB) and amplifies it to drive an output device. For example, my headphones can not be driven by any onboard sound or PCI sound card that I know of. Due to the fact that they're 250ohm.
Rule of thumb: If you're not into production you don't need an audio interface. Get a DAC is that if the case. You don't absolutely need high ohm headphones/speakers either the 80ohm models can produce wonderful sound without requiring as much power. But generally the higher ohm ones will sound better when paired with the right equipment driving them. But there is a lot of snake oil being sold to audiophiles so you really have to do your research.
Even though I have expensive headphones and monitors I don't listen or even mix on them all of the time. Everything I produce gets double and triple checked on some old 2.1 PC speakers I bought in the 90s being driven by a PCI sound card (my motherboard is just old enough to still have a slot for that) and I check everything on crappy laptop speakers too. Laptop speakers are a massive increase in quality compared to something like cell phone mono/crappy ear buds, old 2.1 PC speakers is a massive jump compared to the laptop's built-in speakers, 250ohm headphones being driven by audio interface/DAC is a massive jump compared to that. 99% of people that listen to my work will probably never hear it as I intended it to be heard. 99% of content is produced for the lowest common user (e.g. idiots blaring rap music at full volume on busted cell phone speaker in public on the train). You get the idea.
If you're asking if you need an audio interface AND a DAC/AMP the answer is no. Something like a Scarlett or an MOTU M2 will probably drive anything you have laying around. Although you can't ever be sure if they're supported driver wise outside of the main two platforms those type of devices target (Windows, Mac, maybe Linux). In my case the audio interface I had does work in the *BSDs. But I'm not going to name or suggest it here because it's fairly expensive and I got it for free and I'm not even sure you can buy it any longer (it has A LOT of inputs). I'm not sure if any of the ones I named have proper driver support. Try and see. If there is a Linux driver it probably won't be too much trouble to port it over (or pay someone to port it).
After you get it working have fun obsessing over low latency in the kernel.
Check out the places where the Gentoo studio (or whatever it's called now) guys hang out. They generally have the answers you're probably seeking.
