"The large-signal model is used to determine the DC operating point (VBE, VCE, IB, IC) of the BJT. The small-signal model is used to determine how the output responds to an input signal."
"Use of the large-signal or small-signal model depends on the magnitude of the driving source. In applications where the driving currents or the driving voltages have large amplitudes, large-signal models are used. In circuits where the signal does not deviate much from the dc biasing point, small-signal models are more suitable. For DC conditions and very-low-frequency applications, DC equivalent circuit models are used."
Yes, you are right, but in generaly, you can always use Ebers Moll model in analyse output/input (of course, it isn't many practice is most of cases - equations are very coplex to solvea). For example, audio power amplifier is analysed with model who like as E-B model in many situations:when you find transfer function, factor of distorsion,... Result of linearisation (around DC operating point) E-B model equations is linear equation for small-signal models.