I have just come across these two "doctrines", from reading some online articles. After looking up their definitions on Wikipedia, I have to admit that they seem to be synonyms for the same concept.
Is my inference wrong, and if so why?
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They are different concepts.
Plato in the Theaetetus interprets Protagoras’ doctrine. Plato attributes the doctrine called subjective relativism to Protagoras, that what anyone believes is true for that person, ‘true’ is replaced by ‘true for’. On that interpretation, the way things seem to an individual is the way they are in fact for that individual. If the wind feels cold to me, and I consequently believe that it is cold, there is no objective fact of the matter by reference to which that belief can be false.
Subjective relativists argue that truth and falsity of all judgements and the right and wrong of actions are relative to the beliefs and opinions of the individual thinkers. The view entails that the truth and falsity of our judgements come down only to what we believe or like. Subjective relativism rules out the possibility of disagreement and the very distinction between correct and incorrect judgements, for it turns all our judgements, as long as we believe in them, into correct or true ones. Subjective relativism is a notion that may make critical thinking look superfluous. If the doctrine were true, each of us would be infallible.
Solipsism is the view that only oneself exists. This formulation covers two doctrines, each of which has been called solipsism, namely (1) that one is the only self, the only centre of consciousness, and, more radically, (2) that nothing at all exists apart from one’s own mind and mental states. These are not always distinguished from corresponding epistemic forms: for all we know, (1) or (2) might be true. Epistemic versions of solipsism are themselves extreme forms of scepticism.
In the first type of solipsism, it can be based on the thoughts that one has no direct awareness of the mental states of others, and that to infer that they must have mental states because of the outward resemblance between their bodily behaviour and one’s own is to make an inference based on one case only - not normally regarded as sound inductive procedure. Another, more radical, argument is that one is unable even to form any concept of a state of consciousness that is not one’s own.
The second type of solipsism, which finds problematic not just the existence of other minds but of everything other than one’s own mind and mental states, is a very close relation of scepticism about the existence of the external world. Although closely related, it is not the same thing, since a number of philosophers from widely varying traditions have denied the existence - or at least the independent existence - of a material world, while showing no tendency to assert that theirs was the only mind. Berkeley is a prime example, having portrayed the material world as illusory, wrote a treatise explaining why solipsism was not an inevitable consequence.