There are 16 rooting abilities in Dota 2, from which 6 interrupt their targets.

These 6 use 3 different methods of interrupting.

1. Searing Chains, Nature's Guise, Overgrowth, Entangling Claws: These force a stop command on the unit (as if they pressed S to stop).
2. Ensnare (Naga Siren) and Ensnare (Dark Troll Summoner): These force only the channeling to stop, without affecting anything else.
3. Frostbite: Technically, Frostbite's root does not interrupt at all. Instead, the ability applies the stun modifier.

So this is how they behave against certain orders.

Group 1: Channeling spells completely interrupted, any other order completely canceled, shift-queues cleared.
Group 2: Only channeling interrupted, but hero continues with channeling animation (which delays shift-queued orders). Does not interfere with any of the unit's actions.
Group 3: Channeling spells completely interrupted, any other order interrupted, but unit automatically restarts them, since stuns do not clear unit orders.

This is some unnecessary inconsistency. It would be better if all interrupting roots would do it in the same way. In my opinion, the 1st option is the most straight forward and most clean, while the 3rd option is the worst. The second option would be fine, too, but it needs that one bug fixed where the channel animation does not get canceled.