This effect is due to the effects of parasitic characteristics of the device. A capacitor has four basic parasitics:
Equivalent Series Resistance - ESR:
A capacitor is really a capacitor in series with the resistances of its leads, the foil in the dielectric, and other small resistances. This means that the capacitor cannot truly discharge instantly, and also that it will heat up when repeatedly charged and discharged. This is an important parameter when designing power systems.
Leakage current:
The dielectric is not ideal, so you can add a resistance in parallel with your capacitor. This is important in backup systems, and the leakage current of an electrolytic can be much greater than the current required to maintain RAM on a microcontroller.
Dielectric Absorption - CDA:
This is usually of less interest than the other parameters, especially for electrolytics, for which leakage current overwhelms the effect. For large ceramics, you can imagine that there is an RC circuit in parallel with the capacitor. When the capacitor is charged for a long period of time, the imagined capacitor acquires a charge. If the capacitor is rapidly discharged for a brief period and subsequently returned to an open circuit, the parasitic capacitor begins to recharge the main capacitor.
Equivalent Series Inductance - ESL:
By now, you shouldn't be too surprised that, if everything has capacitance as well as nonzero and non-infinite resistance, everything also has parasitic inductance. Whether these are significant is a function of frequency, which leads us to the topic of impedance.
We represent impedance by the letter Z. Impedance can be thought of like resistance, just in the frequency domain. In the same way that a resistance resists the flow of DC current, so does an impedance impede the flow of AC current. Just as resistance is V/R, if we integrate into the time domain, impedance is V(t)/ I(t).
You'll either have to do some calculus, or buy the following assertions about the impedance of a component with an applied sinusoidal voltage with a frequency of w:
\$
\begin{align}
Z_{resistor} &= R\\
Z_{capacitor} &= \frac{1}{j \omega C} = \frac{1}{sC}\\
Z_{inductor} &= j\omega L = sL
\end{align}
\$
Yes, \$j\$ is the same as \$i\$ (the imaginary number, \$\sqrt{-1}\$), but in electronics, \$i\$ usually represents current, so we use \$j\$. Also, \$\omega\$ is traditionally the Greek letter omega (which looks like w.) The letter 's' refers to a complex frequency (not sinusoidal).
Yuck, right? But you get the idea - A resistor doesn't change its impedance when you apply an AC signal. A capacitor has reduced impedance with higher frequency, and it's nearly infinite at DC, which we expect. An inductor has increased impedance with higher frequency - think of an RF choke that's designed to remove spikes.
We can calculate the impedance of two components in series by adding the impedances. If we have a capacitor in series with an inductor, we have:
\$
\begin{align}
Z &= Z_C + Z_L\\
&= \frac{1}{j\omega C + j\omega L}
\end{align}
\$
What happens when we increase the frequency? A long time ago, our component was an electrolytic capacitor, so we'll assume that \$C\$ is very much greater than \$L\$. At first glance, we'd imagine that the ratios wouldn't change. But, some trivial (Note: This is a relative term) complex algebra shows a different outcome:
\$
\begin{align*}
Z &= \frac{1}{j \omega C} + j \omega L\\
&= \frac{1}{j \omega C} + \frac{j \omega L \times j \omega C}{j \omega C}\\
&= \frac{1 + j \omega L \times j \omega C)}{j \omega C}\\
&= \frac{1 - \omega^2 LC}{j \omega C}\\
&= \frac{-j \times (1 - \omega^2 LC)}{j \omega C}\\
&= \frac{(\omega^2 LC - 1) * j)}{\omega C}
\end{align*}
\$
Well, that was fun, right? This is the kind of thing you do once, remember the answer, and then don't worry about it. What do we know from the last equation? Consider first the case where \$\omega\$ is small, \$L\$ is small, and \$C\$ is large. We have, approximately,
\$
\begin{align*}
\frac{(small * small * large - 1) \times j}{small * large}
\end{align*}
\$
which is a negative number (assuming \$small * small * large < 1\$, which it is for practical components). This is familiar as \$Z_C = \frac{-j}{\omega C}\$ - It's a capacitor!
How about, second, your case (High-frequency electrolytic) where \$\omega\$ is large, \$L\$ is small, and \$C\$ is large. We have, approximately,
\$
\begin{align*}
\frac{(large * small * large - 1) \times j}{small * large}
\end{align*}
\$
which is a positive number (assuming \$large * small * large > 1\$). This is familiar as \$Z_L = j \omega L\$ - It's an inductor!
What happens if \$\omega^2 LC = 1\$? Then the impedance is zero!?!? Yes! This is called the resonant frequency - It's the point at the bottom of the curve you showed in your question. Why isn't it actually zero? Because of ESR.
TL,DR: Weird stuff happens when you increase the frequency a lot. Always follow the manufacturers' datasheets for decoupling your ICs, and get a good textbook or take a class if you need to do high speed stuff.
"Film Capacitor" typically denotes polyester or polymer film as the dielectric - as another answer points out, metallized film capacitors are the same thing: A metallic coating being applied to an extremely thin polymer film, to create the conducting electrodes of the capacitor.
In general, ceramic capacitors are somewhat non-linear in their frequency and voltage responses, compared to film capacitors. Another issue with ceramic capacitors is that they tend to behave as microphones, thus picking up ambient sound and modulating the voltage across them accordingly.
Also, for smaller values (a few pF), ceramics were more commonly used, while larger values were somewhat likely to have film considered as an option - or at least that was how it used to be, before capacitors became so inexpensive with the advent of SMT, that the price difference became negligible except for huge volumes.
Both film caps and ceramic ones are non-polarized, so that isn't a difference.
Best Answer
Multilayer ceramic capacitors (MLCCs) are actually quite good at high frequency operation by the nature of their inherently parallel construction (minimizing inductance and ESR). The type of dielectric used can cause significant variation of capacitance over temperature and applied voltage. Surface-mount varieties can crack under thermal and mechanical stress.
Film capacitors are also good for high frequency, have self-healing capabilities and excel at 'pulse' applications. They're also leaded devices, giving them advantages over surface-mount MLCCs in terms of size (read: higher capacitance values) and durability (they don't crack). The dielectrics used also don't tend to lead to large capacitance variations due to thermal and DC bias changes.
To me, given the choice of a film cap over a ceramic, I'd use the film. Space constraints can make ceramics the only practical choice under some conditions, but I'll use a film anywhere I can make it fit.