space velocities, dwarf vs. giant stars, and GALEX Mira visualization
Re "Sheepspeed reference point" -- there are several common reference frames for measuring space velocities of nearby stars:
(a) relative to our Sun's motion
(b) relative to the "Local Standard of Rest" (google that), the motion of a circular orbit in the Milky Way plane that has the same radius as our Sun's orbit
(a) comes directly from measured quantities: the star's radial velocity, its apparent motion across the sky, and distance. But when I do that I get about 160 km/sec for Mira, so the NASA article's 130 km/sec might be relative to the LSR. Reporting a velocity relative to the Galactic center is certainly possible, but inconvenient -- the star is close to us and far from it -- so an astronomer wouldn't likely do it that way.
130 (or 160) km/sec is pretty fast as nearby stars go. 30-40 km/sec is more typical. (1 km/sec is just about 1 parsec/million years.) So Mira is on an unusual orbit -- most stars stay pretty close to the Milky Way plane, but Mira's orbit must carry it far above and below the plane. It's heading for galactic south at over 100 km/sec.
Re dwarf vs. giant stars, note that a "dwarf" star is just one that's still fusing hydrogen in its core, regardless of whether it's luminous or not, while a "giant" has run out of hydrogen there and is approaching the end of its life (and is generally brighter than it was as a dwarf).
Mira used to be a dwarf star like our sun -- and it's not all that different from how our sun will look in a few billion years. It's a *little* more massive (about 1.2 solar masses, says a recently-updated Wikipedia page). (It has a companion star in orbit around it, so a credible mass estimate is possible.)
At the ends of their lives, when they've run out of hydrogen in their cores, sun-sized stars swell up and go through several giant phases -- Mira is now an "asymptotic giant branch" (AGB) star, a late-phase giant. It's now very swollen, something larger than Mars' orbit, and losing its atmosphere at a great rate.
Rigel and Deneb are also giants -- their core hydrogen has been used up -- but are much more massive than our Sun, so (a) they're 'way more luminous (and were 'way more luminous back when they were dwarf stars too) and (b) their giant phases will end differently -- they'll become supernovae, while stars like Mira and the Sun won't.
Finally, dig this: For the GALEX web site (the satellite that made the observation of Mira's wake), Robert Hurt of Caltech made this lovely artist's-concept animation of how a wake like this might form: