I was going through this link and I found that (on page 8) a practical differentiator circuit resembles that of a bandpass filter. Are they both synonymous?
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No, I do not think that "they both are synonymous".
It is correct that such a real and stable differentiating block will have a bandpass-like frequency response - however, it would be confusing to call it "bandpass", because nobody would use it as a bandpass. Rather it is (should be) optimized for a large differentiating range (with a slope of app. +20dB/dek).
As another example, each amplifier has a limited frequency range for constant gain. But above a certain frequency, the gain will decrease. But nobody would say "lowpass" instead of "amplifier". But everybody knows (should know) about this behaviour.
Comment: It is to be noted that the upper corner frequency is determined by the open-loop frequency response of the opamp. From the question, I got the impression that the described "practical" differentiator would have two capacitors . This is NOT the case. The feedback part can be a simple resistor only which takes care that the loop ain flattens out at the suitable frequency.
