I used to take (sometimes drag) whatever child was in my care to the various Boston museums where I learned a great deal - and some of it rubbed off on the kids. In Boston's Science Museum(and probably most other science museums in other cities) was a demonstration of waves in a cool box. Even better, though I can't find it with an internet search, was a television animated video produced by Ribena (black-currant juice mfr.) about waves that was exceptionally good for explaining them.
Wikipedia's entries on "waves" is pretty technical, but zip through the various entries and you'll get some idea of the different ocean waves.
Wind waves will break if the wind is strong enough. These have no relation with a tsunami, which is a pressure wave. I think you can visualize a wind wave easily, and if you look up the Beaufort scale you can even get lots of illustrations of the size of waves, etc.
A pressure wave is caused by - pressure - think a boat wake, or the up and down movement of water in a water bed. That's sort-of what a tsunami is. An earthquake (or could be a giant meteor landing in the ocean) can cause a vertical pressure wave that forces incompressible water up and down. In the open ocean it's almost unnoticeable, only breaking when the depth of the water is shallower than the height of the pressure wave. (that Ribena video was super at illustrating it). The huge swells or storm surge that can move thousands of miles as the result of powerful storms are similar to a tsunami, though not so large.
So, after all that verbiage - in the open sea, where depths are measured in thousands of feet, a tsunami might not even be noticed. But in shallow water the size and power are devastating.
Here's one link to waves in Wikipedia, and you should be able to follow more of them from each of the entries.
Water Waves, Wikipedia