Christians would lay hands on someone and pray in the name of Jesus, and in some way applying faith in God. It is called faith healing. It is usually done with prayers in the name of God. Sometimes anointing a person with oil along with the faith of the person praying that facilitates the healing.
With Reiki you are not praying any specific prayers, nor are you calling to any specific God. In this sense Reiki is non-religious. On the other hand Reiki is very spiritual in that you are not just dealing with the body of a person, but their mind, and their spirit. In Reiki we are calling on the same force that has created our physical universe and holds it together. This force does not have a gender, nor does it have any specific way to approach it. It is the creative force of life itself. While it is a spiritual concept this is not necessarily a religious concept or a dogmatic one.
In faith healing there are no symbols one must concentrate on. There are no specific hand positions. One simply has faith, and it is this faith that is supposed to move mountains. Faith then in this case is the substance of things hoped for and the evidence of things unseen. It is calling on the promises of healing in whatever faith or religion one aspires to, and believing sight unseen that the things that have been prayed for are being manifested into reality through faith.
In Reiki healing, we use symbols as a catalyst for the Universal Life force to channel through us and help the patient heal themselves. As one progresses in Reiki, often symbols become unnecessary because each symbol has a specific “feel” or energetic signature which can be then called on or channeled. There are specific hand positions in Reiki. These hand positions are aligned with something called an energetic chakra system. Chakras are points along the spine where the human energy has created little whirlpools of energy. When we place our hands along these areas, the idea is to align the energetic system which helps to facilitate wellness and healing.
As to what we call on, we call on the Universal force of life itself, or what is known as the force of Creation. Again there are no particular Deities involved, and no set rules of how to approach such a Deity.
Faith healing and Reiki are similar in that they both produce or affect the ability of the body to heal. There are numerous great stories about the power of faith, the most well-known being the healings of Jesus.
I believe that there are many paths to healing and none should be discouraged. It takes faith no matter which of these paths you chose, it’s simply the methodology that you choose which will facilitate that healing.