Electrical – what is the difference between rated power and power rating

It's not clear what exactly you mean by series versus parallel resistor-capacitor filters. Posting a schematic of each would clarify this.

You probably mean series is something the signal passes thru, and parallel is something that works as a shunt. Note that the same thing that is a low pass filter in series is a high pass filter as a shunt, and vice versa.

Basically a capacitor will block low frequencies and short high ones. If you put it in series with a signal then it is a high pass filter. If you put it accross a signal, it will short the high frequencies thereby making a low pass filter. The value of the capacitance and the resistance it is working against tell you the -3dB rolloff frequency of the filter, whether high pass or low pass. This frequency is:

\$ f = \dfrac{1}{2 \cdot \pi \cdot R \cdot C} \$

When R is in Ohms and C in Farads, then f is in Hertz.

Note that power dissipation is not the only feature which may differ - see below.

You can tell very little with certainty by looking at resistors externally.
Knowing the manufacturer is liable to tell you far more than appearance does.
While I am almost always in agreement with Wouter, and do not differ very substantially on this occasion, I note that in some cases small resistors from a given manufacturer can have larger dissipations than those of larger resistors from the same manufacturer.

An excellent example are the superb SFR16 resistors (originally made by Philips and subsequently sold on several times) and their companion SFR25 resistors.

The combined SFR16 / SFR25 datasheet here shows that an SFR16 resistor is rated at 25% more dissipation than an SFR25 but is only about 50% of the length and 80% of the diameter.
When placed side by side the SFR16 appears tiny compared to an SFR 25, having only about 33% of the volume.

Some other versions of the SRF16 had datasheets that advised up to 0.6W dissipation. (Note that the SFR25H in the above datasheet with the same dimensions as the SFR25 has 0.5 W dissipation).

Why, then, use an SFR25 ever?
The SFR25 compared to an SFr16 has superior temperature coefficient, 250V compared to 200V maximum voltage rating and much superior noise characteristics in some ranges.