The Echo Link is a companion device. It does not have microphones so it cannot be used on its own and needs to be used with other Echo devices or the Alexa app on the same network. You can tell your Echo to play music on the Echo Link, which can then be plugged into your home audio system. It also has inputs for connecting other devices to the Echo Link and then route the audio through it.
The Echo Link Amp does everything that the Echo Link does but also includes a built-in 60W stereo amp for powering passive speakers. Both also include a headphone jack for private listening.
Unfortunately, the prices are on the high side and with their intended use case, these are rather niche devices that aren't for everyone.