There are varying degrees of solipsism that parallel the varying degrees of serious skepticism.
Metaphysical solipsism is the "strongest" variety of solipsism. Based on a philosophy of subjective idealism, metaphysical solipsists maintain that the self is the only existing reality and that all other reality, including the externalworld and other persons, are representations of that self, and have no independent existence. There are weaker versions of metaphysical solipsism, such as Caspar Hare's egocentric presentism (or perspectival realism), in which other people are conscious but their experiences are simply not present.
Epistemological solipsism is the variety of idealism according to which only the directly accessible mental contents of the solipsistic philosopher can be known. The existence of an external world is regarded as an unresolvable question rather than actually false.
Epistemological solipsists claim that realism requires the question: assuming that there is a universe independent of an agent's mind and knowable only through the agent's senses, how is the existence of this independent universe to be scientifically studied? If a person sets up a camera to photograph the moon when he is not looking at it, then at best he determines that there is an image of the moon in the camera when he eventually looks at it. Logically, this does not assure that the moon itself (or even the camera) existed at the time the photograph is supposed to have been taken. To establish that it is an image of an independent moon requires many other assumptions that amount tobegging the question.
Methodological solipsism may be a sort of weak agnostic (meaning "missing knowledge") solipsism. It is a consequence of strict epistemological requirements for "Knowledge" (e.g. the requirement that knowledge must be certain). They still entertain the points that any induction is fallible and that we may be brains in vats. However there are those who say that even what we perceive as the brain is actually part of the external world, for it is only through our senses that we can see or feel the mind. There are thoughts, but that's all that's known for certain.
Importantly, they do not intend to conclude that the stronger forms of solipsism are actually true. Methodological solipsists simply emphasize that justifications of an external world must be founded on indisputable facts about their own consciousness. The Methodological solipsist believes that subjective impressions (Empiricism) or innate knowledge (Rationalism) are the sole possible or proper starting point for philosophical construction (Wood, 295). Often methodological solipsism is not held as a belief system, but rather used as a thought experiment to assist skepticism (e.g. Descartes' cartesian skepticism).