You are correct. Technically the atomic bombs were not thermo-nuclear bombs.
In fact they were quite minuscule in comparison of the true thermo-nuclear devices the smallest of which are several thousand times more powerfull then the most powerful atomic bomb possible.
I don't think any surface testing of thermonuclear devices have been done since Eniwetok and Bimini after which it was decided they were much too dangerous to even test detonate. Definitely not toys and make Hiroshima and Nagasaki look like a child's firecracker. I remember viewing films of the Eniwetok test. Unbelievable. A blast nearly 10,000 times hotter then the surface of the sun and shock waves felt thousands of miles away from the blast, seismic activity recorded for nearly 6 months. An entire Island nearly the size of the UK vaporized and only a gigantic crater deep in the Pacific remains of where the island was. A quantity of sea water equal to the Caspian sea turned to super heated steam in less then one second. Japanese fishing boats 3,000 miles away covered with radioactive ash. weather patterns altered for several years world wide.
I wonder if today's National leaders and military leaders would think twice about wanting nukes if they ever saw one detonated? I doubt if anybody will ever see one in peacetime as to detonate would be world suicide. No person in his right mind would even suggest the surface testing of one.
Stupid for anybody to want a weapon that can only be used for suicide.