Chromium and Chrome differ in a number of ways beyond the name and trademark, though.
Iceweasel is literally just Firefox packaged for Debian, except with a different name and icon. I don't think there is any functional difference (beyond the normal distro-specific packaging that every distro does).
Chromium lacks a number of features that Chrome has, because Chrome comes bundled with a bunch of proprietary components that will never be distributed with Chromium.
A basic example is that Chromium cannot (without a patch) display PDFs in-browser, the way Chrome can. Chromium also cannot support Chromecast, or any of the many other Chrome-specific features, of which there are many[0]
[0] https://i.imgur.com/AIxYzl9.jpg (screenshot is from Firefox, but it illustrates how much Google focuses on Chrome-specific functionality.)
Iceweasel is literally just Firefox packaged for Debian,
except with a different name and icon.
If you read this bug report[1], it's really about more than just a "different name and icon." If they used the official name and icon, they would have needed to have every patch be reviewed by Mozilla, which has serious problems for urgent security patches. And in that discussion, Mozilla voiced concern about several of Debian's patches.
It looks like there has been some effort to do what I've described, come up with a generic default name for Firefox builds that can be used as a default, unbranded version[2] rather than requiring every distro that doesn't want to or can't comply with Mozilla's trademark policy have to do it on their own, but the effort appears to have stalled.
Chromium lacks a number of features that Chrome has,
because Chrome comes bundled with a bunch of proprietary
components that will never be distributed with Chromium.
Sure, I'm not saying that the situations are exactly analogous, just that Chromium has managed to much better avoid the kind of trademark issues with distros that caused so much trouble for Firefox and Debian. On the other hand, as pointed out elsewhere in the thread, it appears that there is no official Chromium trademark policy (at least easily discoverable), but it seems that most distros have been able to use the name without complaint from Google.
It's somewhat trivial, but I remember one change that precipitated Mozilla's complaint was a patch that stopped GIF animation when hitting the escape key. This was years ago though, so I don't know offhand what functionality Debian currently maintains that isn't in mainline Firefox.
Iceweasel is literally just Firefox packaged for Debian, except with a different name and icon. I don't think there is any functional difference (beyond the normal distro-specific packaging that every distro does).
Chromium lacks a number of features that Chrome has, because Chrome comes bundled with a bunch of proprietary components that will never be distributed with Chromium.
A basic example is that Chromium cannot (without a patch) display PDFs in-browser, the way Chrome can. Chromium also cannot support Chromecast, or any of the many other Chrome-specific features, of which there are many[0]
[0] https://i.imgur.com/AIxYzl9.jpg (screenshot is from Firefox, but it illustrates how much Google focuses on Chrome-specific functionality.)