Shamanism is a set of universal spiritual techniques overlaying a belief system. But in any modern sense of the word "religion" it is not a religion.
The ways shamanism is different from religion
Shamanism has no organization other than loosely organized learning circles and organizations dedicated to research. There is no head shaman. There is no book or doctrine. Shamanism is primarily dogma-free.
There is no organized shamanic religion. There's no tithing, no churches, no hellfire.
There are no requirements to practice shamanism or to employ the services of a shamanic practitioner. One can be a Buddhist, or Christian, or nonaffiliated person and still practice.
How are they similar?
In religion and shamanism, there is usually a spiritual intermediary. The shaman, in this case, is the initiated expert who helps one to access spirit. This isn't to say that anyone can't access spirit, but people would usually contact a shamanic practitioner because of spiritual illness or disconnection. The practitioner might help to restore that connection, instead of reinforcing the dependency.
Shamanism includes ceremony and ritual. Ceremony and ritual are important because they address the person at the level of body, mind, and spirit. Shamanic ceremony tends to look different than traditional Western religion, in that it involves the practitioner accessing altered states of consciousness, and traveling via intention and imagination, to other spiritual realms.