They work exactly the same way. All of the popular quadraphonic formats work modulating or encoding the four channels together into two signals which are cut just like a stereo record.

There were/are a great many schemes for achieving the multichannel encoding/decoding all with inherent advantages, disadvantages, and compatibility with legacy equipment. Dolby Pro Logic (and related successor tech) were probably the most successful multichannel tech that people will be familiar with, though that particular scheme came after the heyday of vinyl.