I am looking for a few long range antennas that can pick up signals from recreational drones in the 2.4-2.5 GHz range. I have done a lot of looking online and most of the results I find are for WiFi antennas or other 2.4 GHz antennas.
Antennas in general are not specific to a modulation/protocol/mode, only the frequency range.
It is possible that a device which has "antenna" in the name might in fact be a receiver, or otherwise "smart", but this is not the case for WiFi antennas, and in general anything with a single coaxial connector rather than something more computer-connector-ish is probably a normal antenna.
Some antennas contain built-in receive amplifiers (LNAs). These antennas cannot be used for transmitting, hence would not be suitable for WiFi, and if you did find one, it would be fine for your application but you would need to power the amplifier.
Yes, if you're happy with the antenna's properties (physical size, resonant bandwidth, radiation pattern, feedpoint impedance, etc.), you can use it for other purposes--antennas don't know about "applications".
Two common "gotchas" to watch out for:
Regular Wifi antennas usually have reverse polarity ("RP") connectors that won't mate with normal connectors (the US FCC wanted to make it hard for consumers to use higher-gain antennas on their home Wifi units, so manufacturers complied by using RP connectors). Of the two antennas you link to, one has a normal N connector that's common in RF work, but the other has a Wifi-specific RP-SMA connector that won't mate with standard SMA connectors. You can still use RP connectors, but may need an adapter.
Some antennas have active electronics or other components in them that make them unusable for transmitting (I have a dipole antenna that has a resistor connecting the two halves of the dipole together to eliminate static buildup, for example--trying to transmit through it would be... spectacular...).