This should be obvious, but's not just distance and time, it's also footing and elevation gain loss. I'm certainly not going to be burning 110 calories every mile (as Average_Joes says) because I'm almost exclusively a trail runner. For example, there is one trail that I train on frequently in the summer that is NOT a mountain run. An 8 mile section of it is held as a race every spring. The course record is around 52-53 minutes, and top runners in the race are usually in about 15:20-15:30 or so 5K shape. I often do 15 miles of that trail (there are mile markers) at a good hard pace, it takes me 2:15-2:30. One of the local mountains that I run up several times a year is 5.5-7 miles and 3400-4000ft elevation gain one way depending on where you start. My best 5.5 mile time up the mountain in training is 58 something. A race was held up it and Eric Morse, I think, ran 47 minutes or so. Then there is my favorite training loop, never measured but about 14 miles maybe. At a hard pace (maybe 6:00 smooth level ground pace) I run it in 1:22. But it's taken me long as 3:30 to run in a foot or so of snow. I'm definitely not burning the same number of calories to run that same exact course (except for the snow).
I pretty much don't keep a training log anymore because I'm lazy. If I'm training, I might make note on the calendar of some key workouts. When I do keep a log, I list time and location and maybe some notes like distance if I know it, effort if I'm going particularly hard or slow, tired if I feel tired, etc. But for an everyday type effort, just time and location. I used to keep more detailed logs with mileage, basing it off estimated pace. My ability to estimate pace was usually pretty accurate... I would test when I passed known mileage points and I could adjust for hills too. But basically, it was pointless, just to put a number to a run. Now I ski in the winter, so it's easier just to add up training hours to keep it consistant summer/winter (if I bother to keep a log). Some of it is slow, some fast, but it averages out over a week.