As @Aegolius13 points out, they're the same thing on a 3-engine setup. Different for when there are more engines. Slashy's diagram above best captures the difference:
...Also, note the really critical difference between "asparagus or onion" on the one hand, and "simple" on the other: all engines fire all the time until they're staged away. (By "simple" I mean "the default behavior you get if you just slap everything together in the VAB and don't tinker with fuel ducts or crossfeed options or anything").
For example: Let's say you have a central stack with two radial boosters, all of them liquid-fueled. Let's consider a few possible options:
Option 1: "Simple" staging, radial boosters first.
The ship lifts off on the radial boosters alone (central stack is not yet activated). When the booster fuel is exhausted, jettison the boosters and activate the central-stack engine.
Advantage: Simple to build. Saves the central stack's fuel for the 2nd stage, which is mathematically nice for the rocket equation (it's why staged rockets are a thing).
Disadvantage: The central stack's engine is just dead weight, until the radial boosters run out, so there's a dV hit there. Also, since the central stack doesn't contribute to your TWR when lifting off the pad, it means your radial boosters need bigger engines, which means more dead weight, which means another dV hit.
Option 2: "Simple" staging, all engines together.
The ship lifts off on all three engines. The radial engines burn the radial boosters' fuel; the central-stack engine burns the central-stack fuel. If the radial boosters happen to run out of fuel first, jettison them when they do. Or if all three engines run out of fuel simultaneously, jettison them all together when they run out.
Advantage: Simple to build. All engines participate in launchpad TWR, so you're not lugging any more engine than you need, which saves dV.
Disadvantage: Now you only have 1 stage instead of 2. (Or, if the radial boosters happen to run out first, one-and-a-fraction stages). Which is less friendly to the rocket equation, which costs you dV.
Option 3: Radial/onion staging.
The ship lifts off on all three engines (same as in option 2 above)... but, crucially, the central stack engine isn't using the central stack fuel. It's draining the radial boosters' fuel. As soon as the radial boosters run dry (which will be quicker than in the above options, since 3 engines are sharing 2 boosters' worth of fuel), then jettison the radial boosters and the central engine continues burning, now using its own fuel.
Advantage: Combines the best features of both of the above, and then some. Like Option 1, it has the advantage of being two stages rather than one, which is very friendly to the rocket equation. Like Option 2, all engines are firing all the time, which minimizes dead weight and saves dV. And a third advantage is that it burns through the radial boosters' fuel quickly, which allows you to jettison them sooner and save the dead weight of the booster engines & fuel tanks.
Disadvantage: Requires slightly more understanding of the fiddly bits in the vehicle editor, and about how fuel-flow works. Other than that, basically no disadvantage in this scenario.
Bear in mind that all of the above three options share the common disadvantage that you have radial boosters and therefore somewhat more drag than if you just had one big central stack with a giant engine under it. This is the reason why asparagus staging became somewhat less common after KSP 1.0, which introduced a new aerodynamic model. (For the curious: That's because the old, pre-1.0 aero was simplistic and didn't care at all how parts were arranged on a ship-- it was based purely on mass. Therefore, having radial boosters was zero extra drag compared with having the fuel-and-engine components inline with the central stack, which gave asparagus a big competitive advantage.)
Asparagus still has its uses (I use it fairly frequently myself)-- it's just not the magical unambiguously-better-than-any-other-option silver bullet that it used to be in the old days.
Also note that since 1.2, the improved fuel-flow options in the vehicle editor allow you to build asparagus ships without using any fuel ducts at all, by proper attention to decouplers' fuel crossfeed status, and/or individual fuel tanks' flow priorities. It leads to a slightly less convenient piloting style (you have to watch the tank contents and jettison, since you can't just wait for the radial engines to go dead), but saves you from having to place fuel ducts (thus saving cost, weight, drag, and some editor inconvenience). YMMV, some folks prefer one, some folks prefer the other.Asperagus Staging?
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