You're better off to think in terms of specialized devices to provide the optimum performance of each component in the audio chain.
DAC - this is the same as a
source. In the old days, this meant the turntable, the tuner, or the tape deck. They were all sources and provided no amplification sufficient to drive speakers by themselves. The focus of each device as a source was to provide the highest fidelity possible and preserve and faithfully reproduce everything that was on the music medium. In each case, there was a small amount of pre-amplification and processing that took place within the device (or in the case of phono, industry standard pre-processors). This was done to both compensate for the physical limitations of the medium and to bring the output into a manageable standard that allowed mix and match of standard components throughout the industry (line-level RCA standard).
A DAC does the same thing, but the conversion begins from a digital medium of some sort. The DACs in a CD player, for instance, use the laser CD reader as input. DACs in a television, A/V receiver, iPod or smartphone do the same thing with various media. In the headphone and audiophile industry at large, "DAC" usually means an offboard device that can utilize a digital data stream of some sort - USB, SPDIF, optical, etc. It may still have an amplification stage of some sort - opamp, discrete I/V, etc. Contrary to the popular theory at the time CD's came about (the original emergence of digital media), everything is not simply 90dB S/N ratio and 20-20KHz. The way a digital signal is processed into analog can be all important and each specific implementation's success can vary widely in quality. There is a school of thought recently - fueled by NWAVGUY and others - that is bringing back the view that all's that needed is 90dB S/N ratio and 20-20KHz and things are as good as they can get. More often than not, it's a way to justify a limited investment in one's own equipment rather than any basis in fact. (Yes, I know 90dB is not the goal these days, but it was thought the best ever achievable when CD's came out, especially compared to the 50-60dB of turntables.)
Sound Card - these may encompass a DAC and even a headphone amplifier, but the comparison is like saying a boom box is an audiophile component system. Yeah, it may have all the parts, but it will never compete at the same level. It has always been so in the audiophile world when there were consoles or combination receiver/tape/turntable systems. Yes, you can get great performance sometimes with a sound card, but it will always be hampered by living in the PC environment and using the PC's power supply. A lot of tricks are done (buck-boost circuitry) to make this happen and it can seem like a good alternative, but it will never be as quiet and it will never compete with a truly great desktop amp or DAC. Quite simply, it's physically limited and there's a price for that.
Amp - this is more mixed than one would think than the first two. Most people would think the reverse. However, it's easy to point out that speakers require real power to drive and a sufficient amplifier is needed. With a headphone, it's not quite as clear. Some headphones are efficient enough that a source (with its own internal amplifier) can drive them directly. With others, it's not so clear and you may see the extremes of speaker-amplifier-type-power recommended. Then again, a headphone amplifier can be thought of as a pre-amplifier, where
attenuation is one of the goals desired. So, you can even think of a headphone amplifier being used to provide attenuation. For what purpose, you might ask? To control and preserve the detail coming from the source and at the same time control the drivers in the headphone.
Yes, sometimes that means more power, but often times, it means a better match of amplifier topology with the characteristic drivers. Drivers in the headphones? What's to control, you might ask? Run a test sometime of an amp with a simple resistor as a load vs. a headphone with supposedly equal impedance. They're two different things and may result in huge testing differences. This is why you see such a cottage industry built over esoteric parts (expensive volume pots, stepped attenuators, magic capacitors, and cables, cables, cables). It's all about the optimum match of power-control and headphone drivers.
Just MHO, nothing more ...