Are all spark types occurring for the same reason? Are all sparks the same exact thing, merely created by different means? 
Or are some sparks actually different in some fundamental way? 
There are 3 types of sparks I notice that all look identical but originate for what seems to be different reasons. 
Is there a fundamental difference between a spark from grinding metal (friction based) vs an electrical spark (electrical based) vs a sparkler / firework (combustion based)? 
 A: Not all sparks look identical.
Even sparks produced by the same method, metal grinding, look different for different metals. Hence, spark test - a quick way to identify certain metals or types of steel and iron.
It seems that many sparks involve high temperature, but since they get separated from the source of the heat in small packets, they quickly cool off. Of course, the temperature could be relatively low for some easily ignitable materials, such as metals used in cold spark machines.   
As you've already mentioned, there could be different sources of heat, such as friction, collision, electric current, chemical reactions, etc.
Taking your examples, the sparks generated by a sparkler and a grinding wheel are both burning metal particles and, in that sense, they are similar. However, as mentioned earlier, their trajectory, shape and color depend on the exact composition of a metal and other characteristics of spark generation and burning, at some level, they differ.
When steel is struck by flint, the resulting sparks are also burning particles of metal. They start burning because, due to their small size, the heat produced by the oxidation of freshly exposed surfaces cannot be dissipated quickly enough.   
An electric spark, on the other hand, is produced by the ionized air, i.e., it does not involve solid particles and does not rely on chemical reactions.  
