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For bandwidth, you inject a sine and would expect a sine.
For slew rate, you inject a step and would expect a step (with a slope).
Bandwidth is determined by the poles and zeroes of your system.
Slew rate is determined by how much current you have to charge all caps (real or miller) in your circuit.
Bandwidth is the range of frequencies where your OTA works well considering the Gain. When you exced this BW the gain decreases.
But Slew rate is the maximum velocity of change of signal at the output, usually voltage. It is the capacity of the OTA to follow the input signal amplified. And it is traduced in signal distortion, for example a sinusoidal as a input could result insted of a curves a linear rects, that is distortion.
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