Setting aside inpatient medicine months, we had four kinds of call in our program.
In our first year, we had a multi-week block of night float covering the psychiatric hospital at night (~180 beds). This was done in-house, but a call-room well-stocked with snacks was available. When I went through, it was definitely possible to get a substantial amount of sleep; you got called for restraints, medical emergencies/codes (in which case much of your responsibility was calling the medical hospital across the street and summoning help) and doing things parents do for their children (minor PRNs). You would do this Sunday-Thursday nights
A few months later in order to increase utilization, the hospital started doing "direct admits", meaning patients from distant outlying hospitals in our system could get admitted to the floor directly instead of going through the psych ED as had been the protocol before. You would basically be responsible for inputting all medical orders and doing a medical H&P for people who arrived at 2 AM pissed off and with poor documentation. Super fun. You could have 4-5 of these per night and dangerous things started happening. Not infrequently because we had a geri unit you would get demented patients on blood thinners showing up with basically no accompanying medical records who obviously could not answer meaningful questions about their history.
Also in first year, during our psych ED rotation, you'd do a week at a time of overnight shifts, going from 8 PM to 8 AM Monday-Friday nights. Evening attending would be there until 10 PM and you'd essentially always have a moonlighting senior on shift with you. You were on the hook to steady grind until the end of your shift, but between 3 AM and 6 AM things usually slowed down to the point senior would send you away to take a nap in the other dedicated call room.
In second year, when you were on inpatient rotations, you were on the hook for 24 hour calls when the interns were not available for some reason during the week and would also have to do overnight floor call on weekend nights and weekend coverage for the psych ED. You would also be the "buddy" for interns on the first few nights of night float but could do most of this from home after the first few hours.
The real kicker was when you were on 10 weeks of consults. You and two other PGY-2s would have to split all the overnights and weekends for the block. Overnights weren't so bad, mostly home call with very rare instances of having to come in (patient refusing emergency, life-saving surgery). Weekends were godawful; you would routinely get 10+ consults per day, each of which required a full psychiatric evaluation regardless of the complaint PLUS calling the team to convey reccs + staffing these cases with attendings when they would show up in the afternoon for a while. you would hope and pray that the attendings did not then insist on going and seeing cases with you as things would take so much longer. When you got to 12+ consults in one day you were allowed to call for help and they would pull in fellows and moonlighters from outlying hospitals to take some of the hits.
The floor overnights were kind of worthless as learning opportunities but I do think being overnight in the psych ED was helpful for developing confidence and ability to make decisions with limited information. At the very least I got very comfortable deciding about whether or not I had reason to believe someone met criteria for involuntary hospitalization in our state and declining to pursue involuntary hospitalization if I did not believe they did, even if they expressed SI. I hated every minute of consults so did not feel that way about the call days but this might not have been the case if our program's C&L culture was not as, frankly, OCPD-ish as it was.