Time tracking on an engine is done by the period of time which the engine has been running. The tachometer with an odometer function (tach recording speed, odo recording miles or in this case, hours) fills this function, and actually does very well. When the engine isn't working as hard, it records the hours more slowly.
A "hobbs" or "datacon" is a particular brand of hour meter. It's just an electrical recording device. Hour meter installations may be activated by weight on wheels (squat switch), landing gear position, aerodynamic pressure switches, oil pressure switches, wired in the master switch circuitry, or any number of other means to establish recording of time. The common theme is that unlike the mechanically operated odo on your tach, the hobbs requires electricity.
Recording of airframe time isn't takeoff to landing, and really depends on the airframe. Some want landings, or cycles. Some want total airframe time as recorded by the duration of the flight. Duration of flight is the time the aircraft first moves under it's own power, until it comes to rest after the flight...block to block.
A typical conversion factor for your tach time is about 1.2 to 1.3, depending on how much time you spend at low power during the flight. If you multiply your tach time by 1.2, you'll usually come out close to what the actual flight time has been. Or, you could simply write down the time you fire up and note the time you shut down, and call it good.
You should record the time you start the engine anyway, as it's part of your fuel management; know your takeoff time, your start time, etc. Time your tanks.
Some aircraft installations use separate hour meters for some components in the airplane. While admittedly not a light airplane function, equipment using an auxilliary power source, for example, uses a separate hour meter for that source. How any hour meter is activated, and what it's actually measuring, really depends on the specific installation.