Nope, passing through an object is just the easiest to unterstand way of explaining it without mentioning wave functions. Any energy barrier is subject to that, even the barrier between orbitals.

For those who don't know about quantum tunneling:
In classical physics, if your energy is lower than a barrier, you will never overcome that barrier. That's it, nothing can be done about it, because 2 is always smaller than 3.
What was detected though is that a particle with energy 2 was rarely but reliably detected behind a barrier of energy 3. That is quantum tunneling.

The reason being, that a wave can't just end abruptly, but always has some winding down on the sides. Otherwise it wouldn't be a wave anymore. And these winding down areas can be behind a barrier, if the barrier is thin enough.

This wikipedia animation shows the tunneling happening. The green energy barrier is higher than the wave amplitude, so in classical physic it wouldn't surpass it. But as you can see, when the wave comes close to the barrier there is a smaller wave continuing behind the barrier.

When you now consider that electrons are having wavelike characteristics, where the wave is the probability where the electron can be, this means that the wave after the barrier shows that an electron can, with a small but non-zero chance, move outside its containment. Tunneling through objects is in that regard simply a very, very, veeeeeeryyyyy high energy barrier.