Time-resolved photon detection can be used to generate entanglement between distinguishable photons. This technique can be extended to entangle quantum memories that emit photons with different frequencies and identical temporal profiles without the loss of entanglement rate or fidelity. We experimentally realize this process using remotely trapped Yb-171(+) ions where heralded entanglement is generated by interfering distinguishable photons. This technique may be necessary for future modular quantum systems and networks that are composed of heterogeneous qubits.