There are different models I have seen. I'm a resident and we have a teaching ICU service, but there are also different private services at the hospitals we rotate at that work differently.
For the teaching service, attendings are generally on 7 on/7 off. They are on call for 12 hrs. Depending on patient census and acuity, some are not physically in the hospital for their entire shift, but are available to come in if needed. The night call is divided up amongst all attendings, including ones that are not on service. Most of our people are pulm/ccm so they will bounce between pulm and ccm service, with some preferring one more than the other. So for the teaching service, even if you are not on service, you will likely be covering a night or two and may have to come in for those.
One private group works 7 on/7 off, 12 hour shifts. Someone is assigned to night coverage for the week, but it rotates.
Another private group is 7 on/7 off, generally present during the day and does morning admits. This allows the teaching service to round, and then the teaching service generally does most/all of the evening and night admissions. The private group continues to provide cross coverage for their patients, and would have to come in for emergent needs of current patients, but generally no admissions in the evening. Usually the same guy is on call 24 hrs during the 7 on, but like I said, teaching service generally covers later admissions.
Hospitalists
For academics I've seen 7 on/7 off, and 14 on/14 off. There is generally call Q4 or so. Generally evening and night admissions are staffed over the phone, or the following morning if patient is stable. Attendings rarely come in unless it is super busy.
With private groups, 7 on/7 off. I've seen a few different policies about signing out to the on call guy. Some places once you round, do notes and discharges, you can sign out to the call guy regardless of what time it is. Others its more a traditional 12 hr shift.
I'm sure there are several other variations.