These are the names of the two mathematical algorithms that are used to create the special codes. These are industry-standard algorithms, devised by expert cryptographers. HOTP is less popular, but the device that generates the codes does not need to know the correct time (instead, the codes are generated in a precise sequence). TOTP is much more popular, and generates codes that are only valid for 30 seconds (and so your device needs to know the time). I’d recommend TOTP, as HOTP can be annoying if something causes the sequences to get out of sync.
Posted in: Two Factor Authentication