Are slew rate frequency and cut off frequency same?
They are not at all the same thing.  Assuming we are talking about an op-amp amplifier, the cutoff frequency is the point where the small-signal gain is down by 3dB. 

The slew rate frequency is a non-linear large signal phenomenon.  It has to do with how fast the output can change in response to a large input signal.  It's due to the finite amount of current available to charge/discharge the dominant pole compensation capacitance.

Slew rate limitations will make a sine wave with high enough amplitude and frequency distort to start to look like a triangle wave.