I'm using Chrome 64 and noticed that there's two fields called "memory" on Chrome's task manager. See the picture below:
I can't find any explanation of the difference between these fields on Chrome, there's no tooltips available (at least not on macOS). The "memory footprint" field seems to be new, because I don't recall seeing it before yesterday.
In Chrome, the memory column represents Shared Memory + Private Memory. If you enable those two columns and add the numbers you will find they match the Memory column. In the task manager or activity monitor of the computer you can see that these values match the Shared Memory Size and Private Memory Size.
The Memory Footprint column matches the number of MB reported for the Memory column of the process within the Task Manager or Activity Monitor.
Real Memory in a Mac's Activity Monitor maps to the RSS (Resident Set Size) in Unix. The link below explains this.
https://forums.macrumors.com/threads/memory-vs-real-memory.1749505/#post-19295944
The Memory column on a Mac's Activity Monitor roughly correlates to the Private Memory Size, however it seems to be calculated slightly smaller. This column will match the Memory Footprint column in Chrome.
Please note that this answer references Mac because that's what I'm currently using. The column names and answer would change slightly for Linux and Windows system monitor and task manager.
As Josh pointed out, it reports "Private Memory Footprint" as described in consistent memory metrics
Disclaimer: I'm writing this answer as I do some testing and observation because I had this question myself and this is the only relevant result I found through a Google search. Here goes...
I'm comparing the processes in Chrome's task manager with those in Sysinternal's Process Explorer (for Windows). In doing so, I see that the "Memory footprint" in Chrome is exactly identical to "Private Bytes" shown in Process Explorer exactly for every process ID.
Private Bytes is the size of memory that a process has allocated to it (but not necessarily actively using) that cannot be shared with other processes.
So in line with what Josh and Patrick answered, the memory footprint represents memory reserved entirely for that process.
Unfortunately, I can't come to a conclusion on what "Memory" represents specifically. I would expect it to be equivalent to the "Working Set", but that doesn't match up with what Process Explorer shows.
Things also get a little muddier... If you right-click on the column headers in Chrome's task manager, you'll see there's another column available, titled, "Private memory". If you enable that, you'll see the numbers match very closely, but not exactly to the numbers in the "Memory" column (off by 200K at most). :| This is a confusing title, given that we have already confirmed the "Memory footprint" to represent the private memory footprint.
I don't know what the miniscule difference between "Memory" and "Private memory" here is, but I speculate that maybe either or both columns represent the private memory allocated to the process that are actively in use (in contrast to the private bytes definition I gave above). Or it could be the old calculation that they kept in there for some reason. I really am just guessing here.
Sorry I could not be of more help, but since there seems to be no answer to this out there, I wanted to share what I could figure out and hopefully spur the conversation a bit so someone more knowledgeable can add to it.
