If I'm not mistaken, Kerbal Space Program doesn't model the gravitational pull of more than one stellar body at a time (or is it two?) Needless to say, that sort of discrepancy among other things kind of invalidates it as anything more than a broad learning tool.
Just the one, yes. Whichever "Sphere of most influence" you're in (so getting closer to a body orbiting a larger one suddenly switches you to that smaller one, carrying in your relative velocity from when you were 'just' influenced by the larger one).
Thus the second linked comic (entering a sphere of influence 'in front' or 'behind' suddenly gives you the sphere's core body's influence, whereas in reality you'd already be perturbed towards it whilst still travelling under the major influence of the more-distant-but-more-massive one... and every other planet in the system, to a tiny amount), and there's also no such thing as Lagrange Points in KSP (or weren't, when I last played with it...) and complex resonant orbits between co-orbiting worlds work only by dipping in close to each body with a lot of uncertainty from rounding errors, rather than 'simple' chaos.
But the first comic
does apply when it comes to docking, manoeuvring and otherwise getting close to other items in orbit when there's only the one body involved for the vast majority of the time. As in simply firing straight forward towards another object that you're lagging in orbit increases your orbital potential and causes you to rise above it (I'm looking at you, Gravity! ...even ignoring the whole issue of space-stations likely being on dissimilar orbital inclinations!)), so you either to keep on thrusting and then adjust later (to slow down much more than you were originally moving and 'fall' back onto it) or use at least some thrust to send you Earthwards on a more elliptical path to shortcut the orbit and close the gap from below.
(Easier in the system-view model where it shows your path than when you're doing the "get your Kerman back to your ship" test of the EVA pack, in whatever version of KSP that exists in.)