As of now, what you saw is what you get. I tried to read the abstracts on the ASCO website but all I got was identification and author info. Maybe they are embargoed until the presentation or maybe I have to sign in as an attendee to read them.
As to this one: Minimal residual disease by circulating tumor DNA as a biomarker of recurrence free survival in resected high-risk melanoma patients treated with mRNA-4157/V940, a personalized cancer vaccine, and pembrolizumab
I assume they are taking blood samples from those still alive with no diagnosed recurrence and are looking for cancer tumor DNA circulating in the blood. I would also assume the higher the amount of cancer DNA per unit of measure, the higher the probability that recurrence is brewing. Conversely, the lower the concentration of cancer DNA, the more likely the participant will remain recurrence free, at least for some period of time.
This is all a layperson's supposition. Minimal residual disease means what it says but I have no way of quantifying how big, in cancer-relative terms, that may be. All of this is compared to Keytruda alone, the current standard of care for this kind of patient.
As to the other abstract, I assume "distant" means a longer measurement period. I intend to watch the Moderna presentation on 6/5 (if I remember). I'm confident that will have at least some details from the abstracts if not all of them.