The word congressman has come to be associated mostly with the lower house long ago. The same connotation applies to the gender neutral congressperson though that term came into use much more recently in the second half of the 20th century, according to Google Ngram.
The question is discussed in an article by Neal Whitman on visualthesaurus.com entitled: Election Day Special: Are Senators "Congressmen"?.
The political answer on how the meaning of the word may have grown like this is given in the following excerpt of that article:
So which is the innovation: the semantic narrowing of congressman to just representatives, or the semantic broadening to include senators? The earliest attestation for congressman in the OED is from 1780 (predating the U.S. Constitution by nine years, though coming after the existence of the First and Second Continental Congresses, as well as various colonial and then state legislative houses that were called congresses). Joel Berson, in a message posted to the American Dialect Society mailing list, antedated congressman by three years, finding a 1777 attestation in a Boston newspaper. (The ADS thread begins here.) Boston had a bicameral legislature at the time, and though it's not clear in the passage whether congressman refers to members of only one house, elsewhere in the article it's clear that Congress refers only to the lower house of the Massachusetts legislature.
Congressman does not appear in the Constitution or the Federalist Papers. In searching the Early American Newspapers database for post-1789 attestations of congressman/-men, Berson found examples of the term used to refer to senators and representatives collectively, but also got the impression that "...'Congress-man' was sometimes used, perhaps increasingly gradually during the 1790s, to refer only to a member of the lower house."
The linguistic answer is given in the next paragraph of the same article:
The semantic narrowing was probably inevitable, because of a process known as "Q-based narrowing." Yale linguist Larry Horn coined this term, with Q referring to a principle (first proposed by Paul Grice) known as the Maxim of Quantity. To obey this principle, speakers give as much information as they can truthfully give (while obeying the countervailing Maxim of Relevance by not giving useless details).
So it seems to have gained this word usage somewhere in the late 18th century. I don't think there's a specific reason why the word had to gain this particular meaning. I don't think there is a interesting political answer beyond noting that (professional) writers started (or continued in case this was common in speech, though that may not be as well-documented) attributing this meaning and it stuck over time.