I often see those two terms explicitly used as synonyms, but sometimes from the context I would say they're not. So, is a bypass capacitor exactly the same as a decoupling capacitor?
Yes, decoupling capacitor and bypass capapcitor are the same thing.
These refer to a capacitor located physically close to something drawing power. The capacitor holds the local voltage up for the short time until the current feed can catch up. Due to inevitable inductance of longer lines back to the power supply, the current in these lines takes a little while to change. The purpose of a bypass or decoupling capacitor is to provide the little extra energy during sudden current demands until more current can be supplied from further away.
Since decoupling or bypassing is a high frequency issue, the caps for this purpose must be chosen for low impedance at high frequencies. Their bulk storage capability is not of much importance. In a practical sense, this means they are usually ceramic.
In ye olde days (1980s, or even back into the pleistocene like the 1970s), such capacitors were usually 100 nF ceramic disks. That was about the largest ceramic that was small and affordable. Nowadays, SMD multi-layer ceramic 1 µF capacitors have better characteristics, and are cheap and readily available.
For ordinary use, like around a microontroller or digital chips connected to one, 1 µF ceramic is a good choice. If you're doing RF, then you have to look at the capacitor impedance charts more carefully. I once used a specific model of 100 pF cap for bypassing a RF chip because they had lower impedance at the frequency of interest than other caps with higher values.