The schedule in the Schedules pane defaults to be named by date range, because within MSP everything that happens within the date range is on one schedule file so naming it by date range is most appropriate for the master schedule file (which is what it is in the Schedules pane).
On the Web Terminal, those are Live Schedule Posts, which are really just exported versions of the master schedule, so MSP defaults to name them according to the settings - which ministries it includes, services, etc. It does this because those are the names the volunteers see and that level of description is good for them, since you could potentially create multiple views of the same schedule that each contain different information, like a Live Schedule Post just for EMs or just for Lectors.
It's really just the difference of what is important in the name of the master schedule when you as the administrator see it, versus what is important in a name of a Live Schedule Post when a volunteer sees it online.