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From what I know, the two seems to be the same:

Onion routing: Encryption is done in layers. Alice and server1 exchanges keys and she encrypts her message. Then, Alice and server2 exchanges keys and she encrypts again, creating layers of encryption. Alice then sends the whole layered encrypted message to Bob, and each server will only be decrypt a layer to reveal the address of the other server, which will finally lead to Bob.

Mix networks: Seems to be the same under the description and picture in Wiki, with just the nodes shuffling the order? Is mix network just a subset of onion routing?

What are the differences between the them?

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A mix-net is a combination of proxy servers which bounce all the request into some sort of 'backpack' where anyone can see the whole thing going on but it would be really hard to tell which is which.

Example

We have Mike,Dom, Peter and Jean, they're using a mix-net and each one sends a request to the mix-net. what it'll do is that it'll take all the request, put them into a 'bag' and bounce them all and distributed each message to a new mix node, each of which also had a couple of messages in their bags already. Then those nodes distributed messages to 6 more mix nodes, and those mix nodes opened the messages and distributed them to recipients.

Difference Between a mix net and onion routing

using a mix-net someone could see your traffic but it might be impossible to determine where did it go due to the fact mix-net collects all the messages (http requests) and bounce them all.

another fact is that the mixing will just work if there's more than one message in the proxy server otherwise it will behave like onion-routing with a delay time.

mix-nets don't use encryption on layers as onion routing does.

Onion routing was developed to enable privacy not security thus someone could use a man in the middle between the first node and the last node of your circuit and using a traffic analysis it could find out. your location plus he'll know what you're looking for due to the last node will send the request to the destination without any encryption at all

Summary : if it wasn't because of all the messages,the bouncing and redirection a mix net would work as same as onion routing but without encryption.

For more info read: https://ritter.vg/blog-mix_and_onion_networks.html

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    $\begingroup$ Could you include the main points of the linked article in your answer? $\endgroup$
    – CodesInChaos
    Jun 3, 2017 at 10:49
  • $\begingroup$ Hey I've added what I understood, sorry for the last answer, I was in a rush.. $\endgroup$
    – Graphs Rodriguez
    Jun 13, 2017 at 22:52
  • $\begingroup$ it would be great if there'd be some sort of combination of them.. mix-nets can be affected by a traffic attack that's another difference. $\endgroup$
    – Graphs Rodriguez
    Jun 13, 2017 at 22:56
  • $\begingroup$ Thanks, helped me a lot. So many research papers I read keep saying things like "Mix-net like Tor", but now I know... $\endgroup$
    – Vijay Chavda
    Nov 11, 2018 at 23:41
  • $\begingroup$ Why is there no encryption used in mixnet? If the messages are plaintext, an observer can see where the message is going $\endgroup$
    – Nero Vanbiervliet
    Sep 18, 2020 at 8:50
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Onion routing is synchronous and works per message. Mixing is asynchronous, as the mixers wait for a number of items to be collected

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  • $\begingroup$ Chaum’s mix-nets employ onion routing. A high-latency onion routing should wait to mix the inputs so outputs can’t be trivially correlated by a network eavesdropper. $\endgroup$
    – Shelby Moore III
    Feb 13, 2021 at 22:48

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