pater means father, and mater means mother, and the two words have similar forms.
vir means "man; husband", and fémina means "woman; wife". But the two words look very different from each other. I was wondering if there is a word that looks similar to vir or femina, and means "woman, wife" or "man, husband"?
Pater and māter have the same ending due to an analogy back in Proto-Indo-European, but most kinship terms in Latin don't have that same similarity. For example, frāter "brother" and soror "sister" don't look much alike.
The ones that do look similar can usually be analyzed as a single word that can take different gender markings, like fīlius "son" and fīlia "daughter". Only the ending changes to indicate the gender, just like with an adjective: a good son is a fīlius bonus and a good daughter is a fīlia bona.
EDIT: And as far as I know, there are no general terms for "husband" and "wife", or "man" and "woman", that work like this. There's marītus and marīta, literally an adjective "married", if that suits your purposes, but it's a less common way to refer to a person, married or not.
Many languages use words of unrelated origins to refer to coordinate concepts like "man" and "woman", "king" and "queen", "boy" and "girl" etc. So the fact that vir and fēmina "look very different from each other" should not be seen as unusual or in need of explanation.
The word fēmina is generally considered to be derived from a root that referred to the concept of nursing (also the source of the verb fēl(l)ō "to suck"). Since the root itself refers to a female-associated activity, it isn't likely for a word meaning "man" to be derived from it. (Note that fēmina does not specifically refer to an adult human, but also is the general Latin word for 'female' in reference to non-human animals or even plants. The more specific Latin word for a female adult human is mulier. I posted a Q&A here about the difference).
The word vir appears to have been associated with masculinity from early on, judging from the cognates in other Indo-European languages, but some scholars apparently think it originally had the sense of 'young, youth', per F.J. Ledo-Lemos's answer to Are "vir" and "virgo" etymologically related? Some grammarians allege that a word vira was formerly used with the sense 'woman', but it's not clear how accurate this is. Cairnarvon linked to the two places this form appears in the PHI Latin Texts corpus: Festus's De verborum significatu ("Sed feminas antiqui [...] viras appellabant; unde adhuc permanent virgines et viragines") and Servius's commentary on the Aeneid ("has antiqui viras dicebant"), and it also appears in Isidore, who probably took it from a prior grammatical work ("quae nunc femina, antiquitus vira vocabatur; sicut a servo serva, sicut a famulo famula, ita a viro vira"). There is also the word virāgō but this does not refer to a wife, but specifically to a manlike or manly woman.
The word coniu(n)x, like English "consort", can refer to a wife or (more rarely) a husband.
