This is quite a broad question, since there are far more differences than similarities between the two. This answer will focus on the first part of the question and be about the technical aspects of the two telescopes.
- Basics: FAST is a "classic" filled aperture telescope. This means it consists of a single large dish that focuses incoming radio waves on a single receiver (this is simplified). In contrast, ALMA is an interferometer: Many (> 60) dishes each focus incoming radiation on their own receiver. The relative positions of the individual telescopes is known to great precsion, and both amplitude and phase of the incoming radiation measured, which allows astronomers to combine several or all of the telescopes for a single observation. The maximum achievable resolution is then not determined by the diameter of a telescope but by the distance between those furthest apart. (Again, this is greatly simplified; interferometry is complicated.) In principle, FAST could also become part of a huge interferometer called VLBA.
- Wavelength: FAST is a "classic" radio telescope, observing in the centimeter to meter wavelength range. ALMA is a sub-mm telescope operating at smaller wavelengths of 0.3 mm to about 1 cm.
- Resolution: since the resolution is $
\propto \lambda / d$, with $\lambda$ the wavelength and $d$ the diameter of the telescope, ALMA has a much higher resolution - smaller $\lambda$ and greater $d$. ALMAs resolution is given as 10 milliarcseconds, while in the ideal case FASTs is $1.22 \cdot 0.1 / 500 \cdot( 180 / \pi \cdot 3600) = 50$ arcseconds at 10 cm wavelength. For comparison, according to wikipedia the unaided human eye has a resolution of about 60 arcseconds.
- Atmospheric transmission: FAST observes in a wavelength regime in which our atmosphere is quite transparent. In contrast, the ALMA dishes are located in one of the driest deserts of the world at an altitude of over 5000 m, in order to minimize the effects of water vapour in the atmosphere.
- Collecting area: FAST has a much larger collecting area. Also (I'm uncertain in this point, please correct this if I'm wrong) you lose some sensitivity when doing interferometry compared to just pooling the collecting areas of the single telescopes in ALMA.
- Point Spread Function: The PSF of a single telescope, even a radio telescope, is much simpler than that of an interferometer. So the data analysis required to turn observations into an image should be much more straightforward for FAST.
There are some differences in the required surface accuracy (imperfections significantly smaller in scale than the observed wavelength do not matter) and surface composition - the ALMA dishes are solid metal, whereas the FAST dish is perforated. This works because as long as the holes are smaller than the wavelength, the incoming radio waves see it as solid.
The receivers used to convert incoming photons to electricity for both telescopes work on the same principles. Practically, it is much more difficult for ALMA due to the high frequencies at the edge of the far-infrared spectrum. ALMAs shortest wavelengths are just a little too long for receivers used in infrared or optical telescopes to work, and almost too short for normal radio receivers to work.