You may not even have noticed it, but (on some Macs at least) El Capitan has changed the Energy Saver pane in System Preferences. This may not apply to your Mac, but even Apple doesn’t seem too clear on how this pane should appear on different Macs.
Sixteen years ago, back in Mac OS 9, its Energy Saver control panel offered three separate settings for sleep, each with its own slider: for putting your whole Mac to sleep, including its CPU, and optional separate controls for the display and hard disk(s). For many years I have recommended that users leave their desktop Macs on all the time, and that they should not put hard disks to sleep. This consumes slightly more power, but in return imposes fewer stresses, particularly on hard disks.
So as we have worked through successive releases of OS X, the Energy Saver pane, as it became, has offered similar options, giving you separate controls over the timing of whole system and display sleep, and an option as to whether to put hard disks to sleep. With Mavericks, we gained the added complication of ‘Power Nap’ instead of full sleep.
With my new iMac 27″ late 2015 and El Capitan, these options have been reduced to a single time slider, and whether I want to enable Power Nap, put the whole computer to sleep, and put the hard disk(s) to sleep. I cannot set different times to sleep for the display and the rest of the computer any more. Furthermore, there is no separate time slider for Power Nap.
Back in Mac OS 9, as you have seen, I chose to put my display to sleep after just 20 minutes, and the computer itself half an hour after that. This ensured that the only times my Mac went fully to sleep were when I went out, and overnight. Because of the lack of flexibility in El Capitan’s controls, my iMac now sleeps considerably more than I do, and some days even competes with our cat for the Somnolence Trophy.
If I wanted it to continue making Time Machine backups, downloading updates, and the like, then I could set it to use Power Nap rather than full sleep, but I still have no ability to control that separately from display sleep.
When fully asleep (not in Power Nap), this iMac stops making Time Machine backups, and only wakes to perform system maintenance routines, and when requested over the network.
Power Nap mode, explained in detail here, allows more events to occur during sleeping. Those include making Time Machine backups, downloading software updates, Spotlight indexing, receiving new messages and pushed events (such as calendar changes), and VPN connections using a security certificate (but not those using a password). However, as it does not have a separate time slider control, it too will cut in whenever the display goes to sleep.
It is also unclear from the wording of the controls whether, if you want to enable Power Nap rather than full sleep, you have to check the first box, to prevent the computer from sleeping automatically. As the version of Energy Saver pane shown on my iMac is different from those shown in Apple’s documentation, I can only guess what I should do.
This reduction in features seems inexplicable. MacPilot, working with the preferences file, seems happy to offer separate slider controls and more, although there is of course no guarantee that this iMac will respect such settings. Your mileage, or rather energy saving, may vary.