Putting out a fire and breaking blocks are both actions which remove a placed block from the world. However, putting out a fire is not actually considered a form of block breaking, which leads to some rather odd effects. For example:

• While stat.mineBlock exists for fire (see comments of MC-36191), the action of putting out a fire will not actually increment this value at all. This can be tested simply by checking your statistics after "mining" the fire block.

• It is possible to put out fires in Creative mode while holding a sword or trident, despite the fact that these are programmed to not break any blocks whatsoever (and fire is a block). See MC-30414.

• Breaking most blocks displays the subtitle "Block broken", but putting out a fire displays its own subtitle "Fire extinguished". The only other block to have a unique block breaking subtitle is the turtle egg (see also MC-147246), and also anvils when used up or dropped too much, however both for different reasons. (I personally would prefer a unique translation string for each block being broken subtitle, but that's just me.) Fire's actual material type is wool, whose sounds can be heard when supporting blocks are removed (see MC-91091); this should probably be changed by introducing a new fire material type, so the correct sound plays in such cases.

• There exists no loot table for the fire block, despite most other blocks having one.

There may be other things to test out, but those are just a few.