The difference between the /quote and the /advanced/routes endpoints is that the /quote endpoint will find the best, single step route, select it and immediately generate TX DATA for it -> the one stop shop for transferring token a to token b.
The /quote endpoint is more restrictive. As it only returns one route that can be executed in a single transaction.
While the /routes endpoint will give you a set of routes, single step AND multi step, no tx data, no choosing of the best route.
The /routes endpoint allows more complex routes, in which the user needs to bridge funds first and then needs to trigger a second transaction on the destination chain to swap into the desired asset.
After you get the routes you can get the tx data using the /stepTransaction endpoint. This endpoint expects a full Step object which usually is retrieved by calling the /routes endpoint and selecting the most suitable Route.
Afterwards the transaction for every required Step can be retrieved using this endpoint. Internally both endpoints use the same routing algorithm, but with the described different settings.
NB: The /advanced endpoints /advanced/routes and /advanced/stepTransaction are complex and should not be used directly. Instead, they should be accessed using our SDK