They're similar in some respects, different in others; this happens to only show ways they're similar. Specifically, it only shows dipole (two-pole) fields, with the field lines running from one pole (North or +) to the other (South or -).
But there are also electric monopoles: things that're only + (e.g. protons) or - (e.g. electrons), which'll have field lines radiating out in all directions rather than looping back. Magnets are different in that as far as we know, magnetic monopoles don't exist. Every North pole's directly attached to a South pole and vice versa. You can get magnets with more than two poles, or even more complex arrangements (e.g. refrigerator magnets normally have alternating North and South stripes), but they'll always have equal amounts of Northness and Southness, so the net magnetic charge is always zero.
Another (related) difference is that moving electric charges (e.g. electric currents in a wire) create loops of magnetic field. That is, the field line just goes in a circle around the moving charge, rather than from N to S. Since there's no such thing (as far as we know) as a magnetic charge, that can't happen with the electric field.
I recall an anecdote about a mathematician being asked to clarify precisely what he meant by "a close approximation to three". After thinking for a moment, he replied "any real number other than three".