Is a modern radio wave broadcasting station a very fast spark gap transmitter?
In a spark gap transmitter, is that a "real" radio wave that is
  produced?


It's the antenna that converts the spark induced carrier wave (controlled by an LC tuned circuit) voltage to a radio wave. It does so by matching the impedance of the cyclic voltage and current oscillations (low impedance or low V to I ratio) to 377 ohms where 377 ohms is the impedance of free space or a vacuum.

All radio antennas do this and, without a proper antenna, you will create a "radio" signal that doesn't travel effectively through the medium of space or air because it won't have E and H fields in the correct proportion for an optimized transmission.


  is it a radio wave the same as from a radio station?


It will be a radio wave but it will be an on-off carrier where the on and the off are determined by a morse key that is used to "code" language into dots and dashes: -



After the spark gap circuit and with the invention of valves/tubes, proper modulation (as opposed to on/off keying) could be implemented and radio receivers became much more sensitive. That marks the big difference in tech that emerged and basically the same principles exist today.