Do these circuits work the same way? (capacitors)
Yes and no.

It depends on the frequency components of the current/voltage in the circuit.

The additional traces behave like (low-value) resistors for low frequencies, like inductors for high frequencies, like antennas for very high frequencies, and like waveguides for even higher frequencies.

So for high currents, the resistance may be a problem because of voltage drop.  For high frequencies, the inductance may be a problem because it works against the desired effects of the capacitance.  For the antenna problem, the loop area is important, so in this example the left circuit would have a bigger loop area and thus couple/radiate more.  Whether that is a problem, however, is entirely application-dependent.

For low-current, near-DC, there is virtually no difference.

If used for power supply decoupling, as I interpret it here, it is worth to note that the "aggressivenes"(steepness) of any supply current spikes (from microcontrollers etc.) is more important than the operating frequency of the component.

Rule of thumb: big high-value capacitors are used to decouple high-energy low-frequency content (thus placement is not as critical), while small low-value capacitors decouple low-energy high-frequency content and are placed near the consumer.