The question is, what about the motions of the stars, for instance in our local area of the galaxy? Do they all move together around the galaxy or are some moving faster than others and going “up” and “down” in the galactic plane instead of just moving along in a circle in the general turning of the galaxy? In other words: Suppose the local stars are those little green grapes you put in jello. Does the whole jello mold move, space, grapes and all, or are the grapes more like cockroaches that got into the jello and they are moving every which way, though carried along in the general circle? To further complicate matters, I read in a book once that the local area of stars moves up and down ,above and below the galactic plane, although it takes awhile.

IIRC, they are mostly like grapes, with little movement; but some cockroackes are in the bunch (e.g., Arcturus is going perpendicular to us “normal” star systems).

The majority of stars are orbiting more-or-less in a plane, in a roughly circular orbit, with a speed dependent on distance from the center of the galaxy, so for the most part, stars that are close together will stay pretty close together. However, they’re not exactly in a plane, nor exactly circular, so there’s some in-and-out motion, due to the eccentricity, and some “up and down” motion, due to them not being exactly in the plane. There’s also some stars that are complete exceptions: Barnard’s Star, for example, the second-closest to the Sun at 6 Ly, doesn’t even properly belong to the galactic disk at all, and is just passing through like a bat out of Heaven, on a highly elliptical and highly inclined orbit.

simplication: each star orbits the galactic center of mass, with minor alterations caused by various other chunks of matter. that ours and many nearby stars appear to be acting as grapes in jello is due to 1) similar orbital paths 2) relatively short time span and huge distances involved.