The question's a little more involved than the above, but that's the heart of it. Having reread Unwired and Core, I'm still at a loss as to the difference between requesting data from a node, subscribing to it, and being "in" that node, or even if the latter two are distinct options. For instance, it says in Runner's Companion that if a node in which the AI is running is shut down, it's trapped; does this mean that shutting down any node to which the AI is subscribed is enough to trap it? Also, is logging in/out the same as subscribing?

Any information on how subscriptions, data requests, and presence (if that exists) work would be much appreciated.

An AI has one node that is effectively its current home, much like a person has a node that is generating their persona (typically their commlink). If that node is disconnected from the matrix, then obviously the AI cannot interact with the Matrix.

Subscriptions are dedicated connections to devices. Non-subscriptions are simpler pass-thru connections. You must subscribe to a node to meaningfully interact with it.

Let's say Bob wants to log into Nexus A. Bob and Nexus A are NOT in mutual signal range, but are both connected to the Matrix at-large. Bob, therefore, can connect to Nexus A (assuming he either has its access ID and is authorized to, or it's in Passive/Active mode) by passing through other nodes, much like the internet passes data packets. Bob does not subscribe to any of those other Nodes.

Logging on to Nexus A, though, does open a subscription. This lets Bob's persona interact with the node.

Other things that require a subscription: slaved devices, and any nexus/node to which you're using encrypted comms.

You can 'request data' from a node without subscribing to it, which just means you send the request, and the node processes it, then sends the data back. This would, necessarily, require an authentic account, and the node would have to be set up to handle these sorts of requests (I imagine banking systems *might* work like this, though they might require secure, i.e. subscribed, connections).

think of it as the difference between a text message (data request) and a phone call (subscription). And yes, a subscription means that anyone else also subscribed to that node can see your icon there (tho may need to roll a matrix perception check first if your using some kind of stealth program).

No, according to Unwired, phone calls are Data Requests – except if they are encrypted. Sending a file is a Data Request, even if the file is encrypted.

So, to answer the initial question:

Something you ignore.

A subscription is a sustained high-speed two-way connection. There's table in Unwired that lists things requiring subscriptions. In general, these include drone control links (RC/Jumped In), hacking links (Persona presence), encryption (it's real-time), and slaving. Obviously, not something to ignore. However, the penalties for having too many subscriptions are minor to the point of being ridiculous.

Data transfers and even unencrypted phone calls aren't subscriptions because, presumably, they're more like BitTorrent or asynchronous packeted transfer. It's not a single, sustained, and 'direct' connection.