This answer is for SuSy, the in-house editorial management system used by MDPI. Caveat: I have used SuSy for less than two weeks as of time of writing, and my understanding of it is relatively rudimentary.
Papers in SuSy have their own page, which is much bigger and more detailed than Editorial Manager. It is big enough that I can't fit it in one screenshot.
Manuscript ID: the identifier of the manuscript. It generally starts with the name of the journal, followed by several numbers.
Type: what kind of article is it? A review, a research article, etc?
Open Review: see this article on MDPI's website describing their editorial processes. To quote, "MDPI journals offer the possibility for authors to publish review reports together with their paper (Open Review) and for reviewers to sign their open review reports once “Open Review” (https://www.mdpi.com/editorial_process) is selected by the authors. However, this will only be done at publication with the reviewer’s permission. In all other cases, review reports are considered confidential and will only be disclosed with the explicit permission of the reviewer." If this shows as "yes", then the authors agreed to open review. It does not mean the reviewers will agree to open review.
Recruiting Reviewers: see section 5 of the same article above. The authors, when submitting, can choose whether or not to accept volunteer reviewers. If they indicate yes, then the title/abstract is viewable by volunteer reviewers, and vice versa if no.
Manuscript: the source files for the manuscript.
Section: Some MDPI journals have sections, topics, or similar classifications. If there is such a classification then there will be a corresponding box here. Similarly, if the submission is for a special issue, there will be a corresponding box here.
Author contributions: which author did what for the work? Who conceptualized it, who ran the analysis, who wrote the paper, etc.?
Submission received: when did the submission arrive?
iThenticate: this is an automated plagiarism checker. The report it produces is uploaded here.
Some boxes not shown: There is a section with who the pre-check editor is (i.e., the person that makes the decision whether or not to send the manuscript for peer review), and details of that pre-check. This is also usually the person that will make the final accept/revise/reject decision for the manuscript. There is another box with the APC confirmation. This tells the author what the APC will be should the article be accepted. MDPI offers a lot of discounts, so there is a high chance the published APC is not the one that is actually charged. If there is a discount voucher for the manuscript, this is where to input it.
To search for reviewers you need an email address. Inputting that email address brings up the reviewer profile (the editor can also register a new profile if that reviewer is not already in the system). The reviewer profile gives details like the reviewer's name, affiliation, when they were last invited and by whom/for which journal, whether the reviewer is a guest editor/editorial board member, etc.
SuSy will warn the editor if the invited reviewer shares an email domain with the authors (a little annoying when it flags @gmail.com), as well as things like whether the reviewer is a volunteer, whether that reviewer is being invited too frequently, and so on. The default is to warn the editor if the most recent invitation was within the last 30 days, although this might not apply if the reviewer is a volunteer with a frequency of 1 review per 15 days. If the most recent invitation was within the last 15 days, then SuSy will refuse to send more invitations unless an editor with advanced permissions overrides the block.
The authors can propose reviewers, in which case they are shown here. The pre-check editor (more precise term used by MDPI is "academic editor") can also propose reviewers, in which case they are shown here. Other reviewers are invited by the MDPI editor assigned to the manuscript.
Finally, the green check mark indicates that this reviewer has agreed to review the paper. As with other EMSes, SuSy will display when the reviewer was invited, when the report is due, when the last reminder was sent, etc.
Reviewer/Authors co-authorship: this feature wasn't in Editorial Manager the last time I used it. This lets the editor check if the invited reviewer has co-authored any papers with the authors, and if so what those papers are. It does flag a lot of false positives (multiple people with the same name/initials), which is especially common with Chinese names. If there is a flag then SuSy requires confirmation from the editor before sending the invitation - typically either false positive, or the previous collaboration was more than 3 years ago (3 years is the conflict-of-interest threshold given on the website).
Overall (and this is a personal opinion) I'd say SuSy does some things better than Editorial Manager, and some things worse - with the most important negative being, since each manuscript has its own huge webpage, SuSy is rather unwieldy when trying to monitor the status of every submission in the system.
