No not really. A particle can exist in a general state which is a linear combination of basis states. That is the wave function of the particle can be a linear combination of basis functions. When the linear combination changes, one says that the particle has moved from one state to another state.

The concept of quantum mechanical tunneling is slightly different. One sees that in quantum mechanics there is a non zero probability for a quantum particle to exist, in a state which is forbidden by classical mechanics, possibly for a small time, obeying Heisenbergs uncertainty relations. In terms of the wave function one finds that it can be non-zero where classically it is expected to vanish. Tunneling is a very important physical phenomenon, which has a large number of advanced technical applications.