Okay, let's start.
As an account gotten banned for macoring. People, instantly say that your account is flagged, which isn't right.
The fact, that is your IP under flag. Which means, when a moderator bans your account, he demands your ip and once you are banned on that ip, Jagex take your ip under the control and the look. They do spy on the IP that gotten banned, and see if any account that's running on it is being botted. And if so, they ban it instantly.
I saw people saying, once you get banned, the chance of being banned again is bigger. That's incorrect.
When you get banned, and you change your IP, the chance of getting busted is the same chance that you gotten busted before.
However. By then, your account will be permanently banned.
What jagex does. Is, receive the ips that gotten cough by moderators and take them under their look, to make sure they clear more botters from the game.
Why jagex ban people 2 days?, they see the player is enough active, and have played enough of time, which spent effort on. And they give him a chance to fix what he has done.
As for the first accounts, they ban it instantly because they see that account is a completely cheat for them. And they never give a chance on it.
As for botting on different IP, you can also risk your account (Same as the risk you risked before).
I would suggest, if you care about the account, don't take the risk on it.
Hope I helped,
Best of luck!