This diagram is wrong.
If the capacitor has a "+" on it (some have a "-" ), it is polarized. If there is no sign, it is not polarized. This is always true on the diagram and on the capacitor.
Some electrolytics have NP on the case. They have two positive electrodes, one at each end, with no negative connection lead. They are for AC circuits (such as the crossover of a tweeter in a speaker cabinet). This capacitor symbol has three lines instead of two.
The symbols in the diagram above, going across, should be:
Top row: standard new, air capacitor (old), Leyden jar (or cap with a ground can)
Middle row: polarized new, standard old, variable old, polarized japan
Bottom row: variable new, trimmer new
The old symbol for capacitor has one curved plate because the "new" symbol was (and still is) used for industrial relay contacts (normally open). The curved line lets you know it is a capacitor when both symbols are on the same diagram.
Some capacitors have a ground symbol on one lead. This is not polarization, but for grounding for noise reduction. It is connected to the metal outside can of the package.