Think of the wide range of temperatures that your feet encounter during a day at the beach. The water may seem cold while the sand feels quite warm. The wood on the boardwalk may feel comfortable, but the blacktop in the parking lot is burning hot. Things will heat up at different rates, due, in part, to their different specific heat values. So, as you see, temperature is one of the factors that affects the thermal energy of a substance.
Heat is the transfer of thermal energy from a hotter to a colder object.
An object with at a higher temperature can generate more heat than the same object at a lower temperature, but temperature is only one of the factors that affect the amount of heat an object can transfer. The factors that affect the amount of heat are the same as the factors that affect thermal energy, for reasons that should now be clear to you. Thermal energy is only measurable as heat, during heat transfer. It is important to note that the symbols that are used for the formula will vary from textbook to textbook, but the values that they represent never change. The water in the vat can transfer much more heat, despite the fact that its temperature is no higher that the water in the spoon.