There are two separate settings you need to look at. I don't have a 62, but suspect it will be similar to most other Garmins. First, there will be an item for "tracks" under your settings. This should give you the option to either record/display your track, to record without displaying, or not to record at all.
Then there will be the "track manager" which allows you to view tracks, clear them and save them. So really, you need to visit both of these menus. Use track setup to turn tracking OFF when you finish your hike or ride. This will prevent it from recording a path to your house.
AFTER you have turned off tracking, then you can save the current track and give it a name. After doing so, you would clear the current track - on my Montana, it will ask if I want to clear the current track after I save it.
But the main principle is that you should turn tracking off using the setting menu as soon as you complete whatever ride or hike you want to save. If you follow this procedure every time, the tracks you save will only contain the data that you want.