What is your best definition for the word "decay"? I have seen the word decay used in different ways.
"The uranium nucleus decays"
(seems to mean something breaking into smaller parts)
"the electron decays back to its lowest energy state"
(Seems to mean losing energy)
I would like a precise definition for the word.
 A: Words have multiple meanings, in contrast to mathematical functions, and the meaning depends on context.The same is true for the words used to describe physical observations.
In the context of particle physics decay is used for particles of a given mass which break up spontaneously, because of energy considerations, into smaller mass particles. This also holds for nuclear decays.
The "electron decays back to its lowest energy state" uses the word, in the context of atomic physics, as the fall back of the electron to a lower energy state. Considering the whole atom, the particle physics use of the word holds, because the atom decays from a higher energy state electron to a state of atom+a photon (the energy emitted by the electron falling back). It should be "the atom decays", not the electron. The mass of the atom diminishes with the emission of a photon from the electron transition to a lower level.
There is consistent meaning if the context is considered.
A: A decay is an interaction with one input and more than one output.
"The electron decays back to its lowest energy state" means an interaction of the form $$\text{excited-state atom} \to \text{ground-state atom} + γ$$ or similar. The fact that we tend to describe this as a change in a persistent object ("the" atom) and not as the disappearance of one particle and the appearance of two new ones is fairly arbitrary. Particles have no ontological inertia in quantum field theory; the only reason they persist over time (when they do) is that $\text{particle at earlier time} → \text{same type of particle at later time}$ is an interaction that they can participate in, and often do. There's no fundamental difference between such interactions and the ones called decays; the category of decays is also a human invention.
