Welcome @topherbeats and great work on that privacy guide. 
I think there’s a small piece on this in the wiki, so check that, but also worth reading the topic discussion and pulling nuggets out of that would be worthwhile, if anyone was so inclined 
TL;DR
Tor aims to provide anonymity for people accessing the web and other internet services, and to allow anonymous provision of web and internet services, which are resistant to blocking and censorship. So: anonymity and unhindered access for users and providers / publishers on the existing internet infrastructure. It achieves this through a network of volunteer nodes which obfuscate the endpoints, provide an alternate anonymous DNS, and (I assume) encrypt as much of the traffic as possible. Motivation for providing nodes is largely philanthropic, and carries a small degree of risk because people running those nodes have sometimes been targeted by copyright holders or law enforcement for assisting illegal activity. There have been significant breaches of anonymity by law enforcement, but it isn’t clear if this was due to weaknesses in Tor itself or by other means, but there is significant uncertainty about how secure it is with relation to very powerful adversaries (particularly certain governments).
[I hope that’s a fair summary of Tor - I’m not a Tor expert, so if anyone is, please jump in to correct any errors or omissions.]
SAFE network has similar aims to those I’ve described for Tor with several significant differences:
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it is designed to offer an alternative platform for internet style services, replacing as much as possible of the existing infrastructure with its own services (DNS, routing, SMTP, FTP, http), which are designed to be secure, anonymous and highly resistant to censorship and blocking (including DDoS) from the ground up. So it is not designed to interoperate directly with the existing internet: for example, it’s not for browsing the existing internet like Tor, it is a new very secure internet, that will host websites and other internet services in a secure anonymous, almost completely self contained alternative. However, the user experience will not be so different - existing browsers will access it just with a plugin for example. Run SAFE apps directly from the network, store and load data securely to and from the network with existing apps/programs via a virtual drive mounted on the host OS etc. This approach, secure and anonymous from the ground up, will I believe provid a high degree of confidence in the effectiveness and degree of anonymity provided by SAFEnetwork. Similarly, removing it’s reliance on existing internet services and protocols, and replacing them with a very large number of simple decentralised nodes that perform multiple, frequently changing roles within a constantly changing topology - makes it impractical for almost any adversary to identify, characterise, or block SAFE activity and services.
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being an alternative internet, SAFEnetwork has a much broader remit than Tor - and so includes several other key underlying features from the start (storage, communications, universal anonymous login/identity, virtual drive, web hosting, cryptocurrency, wallet, and application platform), but which will also be extended in time (e.g. smart contracts, distributed computation for example)
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SAFEnetwork is also served by volunteer nodes but these are not reliant on philanthropy, because by providing resources to the network each node is rewarded using the built in cryptocurrency. This token (Safecoin) can in turn can be used to purchase services directly from the network (e.g. storage) or for on network transactions between users and apps/service providers. Being a secure but non blockchain currency, Safecoin can handle very high transaction rates, and scales automatically with the network. It is also designed to be “farmable” by anyone, so easily accessible and widely distributed, rather than becoming centralised.
Well maybe a bit more than a TL;DR! 
Hope that helps.