When exactly does Steam mark someone as 'Online'?

As far as I've found, Steam automatically sets the following status :

Away : Person is logged in but has not been using Steam for 10-15 minutes.

Snooze : Person is logged in but has not been using Steam for 2 hours.

Online : Person is using the Steam client right now. In-game is added to this if the person is also playing a game.

Last Online : x hours ago : Person has logged out of Steam for the last x hours.

Please correct me if that's wrong. My question is, if someone's Steam status is online, does that mean they are currently using the Steam client, or that they are just logged in (Steam is in their computer's system tray next to the clock) ?

You are mostly correct. It's important to note, though, that Steam says you are online if the following conditions are met:

• Steam is running on any machine with your account logged in.

• Steam has detected mouse movement or keyboard usage within the last 10 minutes on any of these machines.

This means that Away can reliably inform you of whether or not that user has touched their keyboard/mouse within the last 10 minutes. Keep in mind Steam does not detect controller input when it determines this. That means if you are in a non-Steam game playing with a controller, then Steam will detect you as Away.

Even if you are in a Steam game and using a controller, Steam will set you to Away - but the "In-Game" status always takes precedence on the friends list so you can only see it if a friend happens to have a chat window open with you. When you go away it will show the message "{Username} is now Away." despite being in-game. This is because Online, Away, and Snooze are actually tracked separately and being In-Game does not overwrite them.

Having an online status on Steam means you are using a Steam client that is currently active. Showing I am playing a NON-Steam game or meaning I am just , for example watching YouTube.

Being logged in means I could have Steam X'd out, but the task is still running (Meaning I closed the Window and not completely ended the task) whilst having any type of status of online, offline, away, snooze, looking to play, and looking to trade.