The Trezor is designed to be a hardware wallet for storing many different cryptocurrencies, but also has many other functions too - including support for acting as a U2F key - meaning that it also works with any site that's compatible with FIDO U2F YubiKey's including BitFinex, Google, Dropbox and many other services.

It can also handle SSH and GPG keys, protecting you against SSH/GPG key theft if your computer / phone etc. was compromised.

Trezor's official wallet only supports about 15 cryptocurrencies, but the Trezor can be used with a lot of different wallets simultaneously such as Exodus (supports about 70 different cryptos via a Trezor), Electrum (a lite wallet which is commonly forked for most Bitcoin-based cryptos such as Litecoin, ZCoin and others), plus more.

The "standard" YubiKey has multiple authentication functions - but the most commonly used is U2F (which the Trezor also supports). U2F is an alternative to TOTP 2FA (google authenticator, authy etc.) using hardware "security keys" instead of code generating applications - and is arguably more secure than TOTP, since a hardware U2F device is much more difficult to compromise than most phones.

YubiKey does not handle crypto though - it's only useful as an authenticator device. So generally, it's better to just buy a Trezor if you need/want a hardware wallet as well as a security key :)