A multi-tank installation usually costs a lot more than a single-tank design and requires a lot more equipment and piping. The advantage is that the layout is a lot more flexible and retrofitting can be much simpler with several small tanks, rather than trying to get one monster tank through doorways.
Both drainback and pressurized systems can use a multi-tank setup for space heating. In either case, the solar loop is the main heat source and the tanks are plumbed in parallel, so they all heat at the same rate and so that heat is removed at the same rate across all tanks.
Plumbing in parallel uses a special technique called "FILO" (first in, last out) or "reverse return" plumbing. This is the same technique you'll use when you plumb collectors together in a multi-panel array: the first panel to get cold fluid is the last to provide hot fluid.
Think of it this way: the cold water enters the first tank, cooling it the quickest. It then goes on to the second and third tanks, cooling them relatively less (and so on, if there are more tanks). The heated water is piped with the third tank (the hottest) closest to the outlet, then the second, then the first.
The practical result of this is that the hot water in the first tank takes longer to reach the outlet but is cooled the quickest by the returning fluid; the water in the last tank is cooled the least but can shed heat the quickest. The tanks are all cooled and heated fairly equally.
You can use a single heat exchanger in a multi-tank system, but you'll need to include a second set of reverse-return piping – one set of pipes brings the heat to the tanks, the other takes it out. The alternative is to use multiple integral exchangers, one per tank: just plumb the solar loop to pass through all the heat exchangers in parallel, reverse-return style.