Koryū and Gendai arts explained.
Gendai budō, literal meaning “modern budō”, or Shinbudō, meaning “new budō are both terms referring to modern Japanese martial arts, which were established after the Meiji Restoration (1866–1869). Koryū are the opposite of these terms referring to ancient martial arts established before the Meiji Restoration. Using techniques that were genuinely used in battle or duelling.

Only martial arts styles that originated and are still run from Japan can be classed as actual budō forms.

An insight to iaidō
In my honest opinion iaidō, is grossly misunderstood and something I wish I had found much earlier in life. There are many iaidō instructors and iaidō schools so check out other genuine dōjō in your area to see what you are more comfortable with.