A Tulpa System is a non-pathological system that is comprised of Tulpas and their Host. Tulpamancy is the westernized adaptation of a closed spiritual practice within Tibetan and Indian Buddhism.  It was introduced by western culture through occult and paranormal circles, entering pop culture through horror stories, and becoming popularized by the My Little Pony community.  Tulpas, according to western interpretation, are entities intentionally created in the mind parallel to your own consciousness.
According to Tulpa.info , Tulpas are intentionally created by imagining a person into the mind and treating them as a real entity. The thought is that treating a Tulpa more like an independent person will help them grow into one. Although, it's unproven whether Tulpas are truly independent or not.  The host can communicate with, interact with, and raise their Tulpa in their mind. The host has a great amount of control over the Tulpa, with the ability to consciously enable or restrict them.  With the host's consent, a Tulpa can also take control of the body. This is called Possession. 
Distinguishing From Other Experiences
Mental disorders: Dissociative Identity Disorder (DID) and Other Specified Dissociative Disorder (OSDD-1) are post-traumatic mental disorders that cause pathological multiplicity. However, it's not uncommon for DID and OSDD-1 systems to mistake themselves to be experiencing something non-pathological, such as imaginary friends, spiritual possession, tulpas, or other forms of non-pathological multiplicity.  This is because amnesia of childhood trauma is very common. Furthermore, many pathological systems are not distressed or even aware of their dissociative symptoms until later in life.  This is why it's very important to talk to a professional if you believe you are experiencing multiplicity in order to rule out pathological causes!
One thing that separates alters from tulpas is that tulpas are intentionally created and alters are not. However, any DID/OSDD-1 system can be under the impression that they intentionally created a system member without knowing that said system member had already existed. Pre-existing alters can come in and out of awareness, or even be pulled into awareness by the upfront alter. An alter revealing themself for the first time, or being intentionally pulled into awareness, can be mistaken for intentionally creating a tulpa.
According to Tulpa.info , tulpas are intentionally made and controllable (the host can consciously change them, restrict them, limit them).  A tulpa cannot take control of the body unless the host allows them, and the host can stop them at any time. Tulpas do not take control of the body like alters do. Alters usually switch involuntarily, especially from triggers. Alters can also switch voluntarily if they want to- but tulpas can never take control of the body unless it’s allowed from their host.  Most importantly, tulpas should not cause any distress, dissociative symptoms, identity confusion, or amnesia. 
The concept of western tulpamancy has gained a somewhat controversial reputation primarily on Tumblr due to how its modern understanding was derived from Tibetan and Indian Buddhism. Some circles believe that it's culturally appropriative to be using the term "tulpas" or "tulpamancy" outside of their religious context, and opt to use different terms instead such as "thoughtforms" and "parogens."