Tony,
Functionally, in some cases, perhaps. Physically, no.
A battery holds its charge via a chemical reaction of one type or another. A capacitor holds its charge by mounting two charged plates in close proximity with a dielectric material (one that resists electron flow) between the two plates. One of the two plates is then crammed full with lots & lots of electrons (the more electrons on the plate the greater the voltage potential between the two plates). The electrons want to get to the positive plate and so will do work in a circuit to get to the other plate.
The big upside to capacitors is that they can supply all of their power essentially instantly, whereas batteries' output rate is limited by the speed at which the chemical reactions can take place (and the battery case can deal with any gasses or heat generated). It is this ability to discharge a lot of electrons rapidly that makes capacitors so potentially (pun intended, thank you) dangerous - think Loren's TV capacitor discharge story.
Capacitors do, however, tend to leak electrons from between the plates, making them less suitable for long term power storage. There are exceptions to this rule, but they're mighty costly options when compared to batteries which can maintain their charge stable for upwards of 10 years (depending on the specific chemistry & storage conditions).
Charging capacitors is a more efficient business as you don't have as much loss, so that makes me think they may be used in watches (as the work gathered from a motion mechanism must be in very small increments to begin with).
That being said, I'm not a jewler so have no idea whether the watch in question was a battery or a capacitor.
-Zeke
ps - If you already knew all this Tony, I apologize.