"Ripping" wood is where you cut strips along the length of a board (this is generally done with a table saw and a "fence" set at the distance from the blade of the width of rip. You could also do it with a straight line and a power hand saw. As you said, it goes along the grain of the wood. This is what you want for your top bars.
A "cross cut", as the name implies, goes across the grain. If you cross cut a thin strip, it is generally not going to be very strong because you have cut across all those grains and it will be somewhat brittle.