Yes, they are waves, but they are often very long waves. A typical 1m wave might be 20m long. A tsunami wave might be a kilometer long or longer. That is why people say they are like a tide. The wave arrives, then does not recede for several minutes. So, while a 4m wind driven wave might break over a seawall and even wash a car off the road, a 4m tsunami washes ships over that same seawall and floods the city.

It’s a wave, but it is often not at all like a regular ocean wave. I’ve been at sea when a 3m tsunami passed, we barely felt it. If it had been a 3m wind wave in that otherwise calm sea, it would have knocked dinner off the table.