Sense of agency is the subjective awareness that one is initiating, executing, and controlling one's own volitional actions in the world; that is, the sensation or awareness that actions and thoughts are of one's own intention. Sense of ownership is the pre-reflective awareness or implicit sense that one is the owner of an action, movement or thought.
Because these terms are fairly well defined on the wikipedia page, this article will focus on how these terms relate to tulpas and tulpamancy, and hopefully help clarify the subjective experience of certain practices.
Tulpas and other thought-forms
A thought-form can only be considered a tulpa when the host has no sense of agency or sense of ownership over it and its actions. That means that when a tulpa does something, says something, thinks something, those thoughts and actions are perceived as coming from somewhere other than the host's mind, and without the host's volition or intention. In other words, the tulpa's actions feel alien, as if they are the actions of a separate individual (many people refer to this level of development as independence).
A mind-form is the way in which people perceive themselves, and therefore no change in sense of agency or sense of ownership occurs. An alternate mind-form may include additional limbs or appendages, creating new perceived parts to have sense of agency and/or ownership over.
Switching is the act of consciousnesses (tulpa and host) exchanging control over the host body. Sense of agency and sense of ownership of the body are switched to the consciousness in charge of the body.
Possession is the process of a non-dominant consciousness (typically a tulpa) taking sense of agency over part or all of the host's body. Sense of ownership is not necessarily affected, the host may also lose sense of ownership over the part(s) of the body affected.
Proxying is the process of acting as an intermediary for a tulpa's communication. The host does not lose sense of agency or sense of ownership of any part of the body when proxying, unless possession is also involved.
Merging is the process of combining two or more consciousnesses, the sense of agency and sense of ownership of the body also transfers.