Machi vs chimata
So a while ago Claytonian wondered what the difference between machi 街 and chimata 巷 was, since both can be translated as "the streets" and coupled with no akari to mean "lights of the streets" or "city lights." Let us examine the issue.
Etymologically, chimata comes from /ti/ "road" + /mata/ "fork," thus, a fork in the road, a crossroads. And, just as settlements and commerce tend to build up at crossroads, it eventually came to mean "streets [where people do business]" and, more metaphorically, "society" (e.g. chimata no uwasa, "word on the streets," "the word").
Here's a cool old poem (MYS 11/2506) featuring chimata in a less metaphorical way:
事霊 八十衢 夕占問 占正謂 妹相依
Kotodama no/ yaso no timata ni/ yuhuke tofu/ ura masa ni noru/ imo ha ahiyoramu
I went down to the (eighty-forked) crossroads where the kotodama dwell
And heard the news that the one I love, she loves me back as well
[Something something hoistin' my palanquin since I been gone]
(May have embellished that a bit.)
Machi, on the other hand, has an unclear etymology (maybe /ma/ as in "space" and /ti/ as in "road," or as in "earth"? opinions are divided) but in its earliest attested usage already refers to a division of land — as in, a rice field. This was inevitably expanded to refer also to subsections within palace and mansion grounds, and then to a concept roughly corresponding to "city block."
So a machi is a concrete thing. It is a sub-place, implicitly subordinate to a super-place; an area where things are. A chimata is not so much an area as a point through which things pass. A machi is an object; a chimata is a system. Thus, although the two words do have a synonomic overlap, chimata also covers some abstract, figurative territory which machi cannot reach.
Also, pragmatically speaking, because machi has been repurposed many times over the years to refer to specific configurations of streets and buildings, it has a more down-to-earth feel than chimata, which as far as I know has never been assigned a specific definition. Thus, chimata has a slightly more poetic flavor.