If the second character is in follow mode or standing around worthlessly until tabbed to and given a command, then both characters are
not in control at the same time. This is "multiboxing", but not illegal or unethical multiboxing(per Blizzard's ToS), as long as only one character is being controlled at one time. But some people define the second as the entire definition for the word. You could argue that it's still lore breaking, unfair, unethical, unrealistic, etc, to do anything combat related(or run them at all), but using Blizzard's original rules(in the ToS); it didn't matter how many you ran at once, or what you did with them, as long as no bot or "third party program"(Anything that's not the game client) was used to control them. A player could only control one at a time legitimately without such a program.
Of course, they didn't actually enforce their own rules, so it didn't really matter. You could quote the ToS to their own face and the guy you're reporting that's 5 boxing bot soloing dungeons/arenas would not be punished. They opted instead to just take the extra money from people doing it(sells out, as always). You see, on retail, doing this meant doubling up your WoW costs, buying boxes+subs for each account. They probably enjoyed that extra money. I bet to this day players still do it freely, especially since most expansions have now been rolled into a single cheap purchase. You mainly just have to pay for the stacked subs.
On a private server, it would be much more problematic because there's no extra cost to stacking accounts and running WoW at this point on an old patch is not exactly taxing on modern computers. I could probably run 5 of these myself if I wanted to, just reduce the resolution/graphics of all the extra boxes then let whatever program is playing them worry go to work. But I am against such cheats. I only use a second character in legitimate ways(alt tabbing). Ultimately however, it's up to the server to decide what they allow or don't allow. A server writes its own ToS and decides what to enforce. They could say "NO" to any notion of even having more than 1 character logged in at once, or allow it if it is not used in any combat related way(such as healing yourself). Or they might be like Blizzard and not give the slightest shit what you do. So far, it looks like both Nostalrius and Kronos are allowing multiboxing, as long as no program is being used to control characters, as Blizzard originally claimed(but never really) supported.
I used to dual box off one of my relative's accounts mainly to talk to the opposing faction. That was incredible fun on a PvP realm. When I went on killing sprees with Rogue alts(ie L29), what I liked to do was park a character on their side in the same zone so I could see myself being complained about or condemned in their chat. My twink Rogue killing Alliance newbs was notorious in Duskwood and Redridge for a while. He lived in those zones, and killing Alliance newbs was his duty. The low level character on their side would have a nearly identical name, so sometimes I'd drop into the chat to say something funny when people kept calling it out everyday. When a high level skull con showed up and said something like, "ok, back on my main, where is he?" I'd say in their chat, "They see me gankin, they hatin". They'd run around on their mounts trying to find me. I'd say something like "Check unda da tree stum mon". Fun times. I was there so often just quietly reading the chat was great. People would say things like "Is this guy here everyday? Doesn't he have anything better to do? He could have been 60 by now." Or "Ya he's here all the time. You solo quest that graveyard at your own risk. Newbs beware." "His chatalt is online in the zone, that means he's here, fyi. When you don't see the chatalt online anymore, that means it's safe."(Sometimes they got smart) "Rogue ganking at orc fort again, same guy as usual." That's when you drop something like "For the Horde!". If you did this as a Dwarf twink, talking as a Dwarf in the Horde chat would have been hilarious. Ever read the Flintlocke comic? Talk like him in the Horde chat.
http://pc.gamespy.com/articles/578/578734p1.html