Nice jokes :p
OTP means one-time password. It's an evolution of the traditional password, which is static and many ppl repeat the same password on multiple services and portals.
OTP uses a seed, which is stored on the OTP client, which may be a software like KeePass or a hardware. It's one-time because the seed is used as input to generate a limited-time password which becomes useless then. Normally it's a 6 digit number, but it may be 8 digits. It also prevents repeating the same password, because it's the server that generates the seed, therefore users can't repeat it.
HOTP uses a counter as the other input to generate the code, I've never seen it being used. TOTP uses current time as input, therefore requiring both server and client to have precise time set. The most popular TOTP client is Google Authenticator, but it's not good because it's proprietary software. There are some FOSS available, KeePass is great.
The advantage of TOTP is that it can be used with a free software, as I said. There's no disadvantage of TOTP over plain password and there's no reason to not use TOTP in place of plain password. The problem is that, when it's being registered, the seed is shown in plain text, even when it's on a QR. At that moment a malware is able to capture it and a hacker use it to get access.
FIDO is the solution for that. It's an open standard designed by an alliance of companies, aimed at solving the authentication vulnerabilities that still remained. AFAIK it doesn't accept a software client and requires buying a device, we have a handful of companies that produce a variety of models. It assures privacy as no user identifiable data is sent to server.
It's based on asymmetric encryption, the private key is generated on the device and never leaves it, and each account uses different private key. Data is encrypted between the device and server, therefore anything intercepting the traffic is unable to read it, even if HTTP is used without SSL or TLS.
Of course it has the disadvantage of having to buy a device, which becomes expensive on some places of the world. But as many companies implement FIDO support, this price is diluted among all accounts we secure and over time.
Some ppl say that FIDO is enough and can be used passwordless. Still, most portals I had seen use it as a 2FA and keep the password.
