The word "coherent" is used in Physics in a rather sloppy way. Your first state is a linear combination of harmonic oscillator eigenvectors that turns into a gaussian in momentum/position representations. In a more general background, a coherent state is just a state where coherences (off-diagonal terms in the density matrix) are non-zero, which means the state can skipp from one stationary state to another.
Now, a coherent superposition is quite like a coherent state: a superposition is said to be coherent if there's an observable that, if applied to one state, can turn it into another also present in the superposition. As an example, consider the $z$-axis spin up and spin down states of the electron in a Stern-Gerlach experiment. Then there is one spin operator, namely $S_x$, that can turn one into the other. This means they form a coherent superposition. As a counter-example consider the ground and the first excited states of the harmonic oscillator: the creation operator can turn the former into the latter, but this operator is not an observable. The superposition is a non-coherent one, meaning that off-diagonal elements in the density matrix are irrelevant to the problem at hand.