supposition vs conjecture

supposition and conjecture both are nouns.

Word	Noun	Adjective	Verb	Adverb
supposition	Yes	No	No	No
conjecture	Yes	No	Yes	No

As nouns, conjecture is a hypernym of supposition; that is, conjecture is a word with a broader meaning than supposition:

supposition: the cognitive process of supposing
conjecture: reasoning that involves the formation of conclusions from incomplete evidence

As nouns, supposition and conjecture are synonyms defined as:

supposition and conjecture: a message expressing an opinion based on incomplete evidence

Other synonyms of supposition include guess, hypothesis, speculation, surmisal, surmise.

supposition (noun)	conjecture (noun)
a hypothesis that is taken for granted	a hypothesis that has been formed by speculating or conjecturing (usually with little hard evidence)
the cognitive process of supposing	reasoning that involves the formation of conclusions from incomplete evidence
a message expressing an opinion based on incomplete evidence	a message expressing an opinion based on incomplete evidence

supposition (verb)	conjecture (verb)
	to believe especially on uncertain or tentative grounds