We've all seen videos on video.google.com or youtube.com of people
microwaving a match covered by a jar. What exactly is happening to
cause that reaction? It was referred to as plasma. Is this accurate?
This isn't the same plasma that's in my blood, is it? Is this at all
related to ball lightning?

The plasma in blood isn't the same thing as what's present in a match
flame. Blood plasma is the fluid which carries the blood cells
throughout the body. Plasma in a flame, on the other hand, is a gas at
a temperature high enough to strip electrons from the atoms scattering
off each other in the gas. This ionises the atoms, giving them a
positive electric charge. The gas will then respond to applied
electromagnetic fields.

   Ball lightning is related, since it basically amounts to a mass of plasma.

I'm curious why they're both called plasma because they don't seem at
all related. Are there any shared characteristics between the two
types that could explain that?

Reportedly, use of the word "plasma" in reference to ionized gas was
coined by a gentleman by the name of Irving Langmuir, who was doing
electrical research during the 1920s. The following is quoted from
this webpage: http://www.plasmacoalition.org/what.htm...

"During the 1920's Irving Langmuir was studying various types of
mercury-vapor discharges, and he noticed similarities in their
structure - near the boundaries as well as in the main body of the
discharge. While the region immediately adjacent to a wall or
electrode was already called a "sheath," there was no name for the
quasi-neutral stuff filling most of the discharge space. He decided to
call it "plasma."

While his relating the term to blood plasma has been acknowledged by
colleagues who worked with him at the General Electric Research
Laboratory, [1], [2], the basis for that connection is unclear. One
version [2] of the story has it that the similarity was in carrying
particles, while another account [3] speculated that it was in the
Greek origin of the term, meaning "to mold," since the glowing
discharge usually molded itself to the shape of its container. In any
case, it appears that the first published use of the term was in
Langmuir's "Oscillations in Ionized Gases," published in 1928 in the
Proceedings of the National Academy of Sciences [4].

Thus the term "plasma" was first used to describe partially (if not
weakly) ionized gases. The term plasma apparently did not find
immediate widespread use in the scientific community. It did
eventually catch on, however, but in some cases the term was
inappropriately limited to highly ionized gases.

REFERENCES

[1] L. Tonks, "The birth of 'plasma'" Amer. J. Phys., vol. 35, pp. 857-858, 1967.

[2] Letter from H. M. Mott-Smith to A. M. Bueche, Apr. 20, 1967 (on
file at Communications Operation, General Electric R&D Center,
Schenectady, NY).

[3] S. C. Brown, "A short history of gaseous electronics," in Gaseous
Electronics, vol. 1, M. N. Hirsh and H. J. Oskam, Eds. New York:
Academic, 1978, pp. 1-18.

[4] I. Langmuir, "Oscillations in ionized gases," Proc. Nat. Acad.
Sci. U.S., vol. 14, p. 628, 1928; also available in The Collected
Works of Irving Langmuir, vol. 5, C. G. Suits, Ed. New York: Pergamon,
1961, pp. 111-120."