I usually see Eb/No used for BER curves.
Fundamentally, SNR refers to bandwidth (signal power vs noise power in a certain bandwidth) and can be measured for both analog or digital modulations. Eb/No refers to bits (energy per bit vs noise per bit) and is only relevant to digital data streams. SNR is commonly used when the data is modulated because it can be measured without knowledge of the underlying modulation. For instance, if you received an unknown signal, you could observe it's spectrum and estimate the SNR. Without demodulating (or at least knowing the modulation) you could not calculate Eb/No.