What is the main difference between v3 and v4 in this topic?

In bt.v4, tickExactlyOnce calls tickRoot(EXACTLY_ONCE, std::chrono::milliseconds(0));
which will behave the same way tickRoot in bt.v3

In bt.cpp 4 you have other options to tick (e.g. TickOption::WHILE_RUNNING); usage tree.tickRootWhileRunning()

Thanks for answer. Is good to know, but there are some questions related.

About tickOnce method, that implements tickRoot(ONCE_UNLESS_WOKEN_UP, 0s)?
What happens if there is a BT node that emit a wake signal? will it needs to wait for the loop rate?

yes, that is why you have another inner loop:

  while(status == NodeStatus::IDLE ||
        (opt == TickOption::WHILE_RUNNING && status == NodeStatus::RUNNING))
  {
    status = rootNode()->executeTick();

    // Inner loop. The previous tick might have triggered the wake-up
    // in this case, unless TickOption::EXACTLY_ONCE, we tick again
    while(opt != TickOption::EXACTLY_ONCE && status == NodeStatus::RUNNING &&
          wake_up_->waitFor(std::chrono::milliseconds(0)))
    {
      status = rootNode()->executeTick();
    }

if you use tickExactlyOnce it will wait the loop rate to tick again;
tickOnce will tick again if you have a wake_up signal.

StatefulActionNode and Threaded ones may emit a wake_up signal.
You can check the SleepNode for example