David
I spent two years reviewing images of culverts, those images are better than a number of the professional ones I got from CCTV mounted on ROVs. Also those drains are in far better state than a number of the ones I saw.
Looks like the 24" CI is socket spigot pipework possibly cement lined and in good nick, the alignment may be a bit off straight but there is no major obstruction by tree roots or similar.
The square section either has a lot of water in it, is silted up or the watercourse steps down into the lead pipe beyond. Be careful if you seek to take the silt out of the bottom to check there is a firm invert to the culvert, it is not unknown for there to be just walls and a roof in such circumstances and you don't want to undercut the walls. Is there any sign of a manhole at the change of construction which would be normal?