I have found quite a bit of information on the UCC ansatz, but I cannot really find basic explanations for the Ry and RyRz ansatzs... Are they just applying these gates to a circuit? If anyone has good material on this I would greatly appreciate it!
In term of the $RY$ Ansatze, from my understanding, this is because many systems of interest, the Hamiltonian contains only real terms. And if we have real Hamiltonian, then the decomposition of the matrix representation of the Hamiltonian can be achieved with real eigenvectors.
Now, a single-qubit $RY$ rotation confined the qubit state remains real. That is, it is restricted to the $xz$-plane. You can see this through the Bloch-sphere visualization below.
Furthermore, if we use CNOT as our entangling gate operation, then it has a real representation. Thus if we restrict our single-qubit operations to leave each qubit state in the real subspace then the state as a whole will be in real. This is why, people consider the $RY$ ansatze:
┌──────────┐ ░ ░ ┌──────────┐ ░ ░ ┌──────────┐ ┤ RY(θ) ├─░───■────■────────░─┤ RY(θ) ├─░───■────■────────░─┤ RY(θ) ├ ├──────────┤ ░ ┌─┴─┐ │ ░ ├──────────┤ ░ ┌─┴─┐ │ ░ ├──────────┤ ┤ RY(θ) ├─░─┤ X ├──┼────■───░─┤ RY(θ) ├─░─┤ X ├──┼────■───░─┤ RY(θ) ├ ├──────────┤ ░ └───┘┌─┴─┐┌─┴─┐ ░ ├──────────┤ ░ └───┘┌─┴─┐┌─┴─┐ ░ ├──────────┤ ┤ RY(θ) ├─░──────┤ X ├┤ X ├─░─┤ RY(θ) ├─░──────┤ X ├┤ X ├─░─┤ RY(θ) ├ └──────────┘ ░ └───┘└───┘ ░ └──────────┘ ░ └───┘└───┘ ░ └──────────┘
Also note that this Ansatze has the name "Real Amplitudes" in qiskit. This is because what I described above.
Now, $RY$ rotation follow by $RZ$ rotation will allows you to get more general quantum states, states with non-real amplitudes. Thus this Ansatze, $RYRZ$ Ansatze, is aiming at a more general setting. But if you consider chemistry problem then most likely you should be able to get away with just using $RY$ Ansatze.