As with all applications of language on physical phenomenon, the definition of spark is so broad and general, it almost has no meaning at all. I would guess its meaning to most people is just something like a pointlike flash of intense visible light, which can be caused by a whole litany of things. Probably, most people see the sparks in fireworks/sparklers when they think of it, which are most of the time pieces of metal containing particles at really high tempeartures, which are hmx's forte.
However, you must remember to separate the idea of temperature with heat, like how most people should stop thinking high voltage or high current is automatically dangerous. While the temperature of that spark might be really high, it has such low total heat, that it does you no harm when it falls on your arm when handling a sparkler; by the same token, when you make a spark by touching a doorknob on a dry day, you are involved with high voltage but with a tiny amount of actual flow of electrons.
Interestingly, plasma is the predominate form of matter in our universe because it is the natural form of matter in environments of intense energy, as in stars. But sometimes I wonder, if those astronomists are just assuming everything that is in the universe can be seen, which limits things down to radiation emitting objects.
Yes, plasma can be controlled by using electric or magnetic fields, because they are defined as excited collection of positive and negative ions. Problem is with making a controlled stream from a sparkler is that by being excited, they are giving off their energy/heat all the time. You are sitting in a bath of relatively cool fluid while the sparkler is giving away its chemical energy as heat and light. For a sustained production, you need to keep adding energy. And that spark has just used up its own energy in a pretty much irreversible reaction.