Are the Total Hours and Total Cycles of an aircraft based on the Flight hours or Operational hours of an aircraft?
One takeoff and one landing makes up one cycle. Counting cycles is important to keep the number of times the cabin was pressurized (with the assumption that the airplane flies at high altitude). It is also significant for engine maintenance. A cycle and flight/operation time are not related.
This is the time when an airplane is in operation (more on this below).
Generally speaking, it is the time when an airplane is flying. It is the duration from when landing gears leave the ground to when they touch the ground again. Pilots are not paid by this. In my opinion, it is mostly used by flight trackers to inform people if an airplane has landed or not.
For GA airplanes, when the airplanes is started, Hobbs meter starts and it stops when the engine is turned off. Most commonly, this is how rental GA airplanes' rent is calculated.
For commercial airplanes, pilots pay clock starts when parking brake is released and ends when the parking brake is set.
Hence, total hours is more closely related to operation time.
If you are talking about total time and total cycles in reference of retiring an airplane, that is a different discussion. Each part of an airplane has a certain life. Though most of the time it can be predicted, but sometimes a certain component fails earlier than the expected life and therefore needs to be replaced. Airplane manufactures do specify a design life limit, but that is normally changed because of regular maintenance.
I'm not sure about the total hours but cycles is based on take offs and landings. As per this article
the cycle count (takeoff and landing is considered an aircraft "cycle")
They also go on to say
or the number of hours flown since the last check
so I'm guessing it's flight hours. For what it's worth in small GA planes this is generally measured with a Hobbs meter which clocks hours based on the engine running. That does not mean you have left the ground. So any hour based service on a GA plane is going to be done on that clock not a flight time clock (which none of the planes I fly even track).