The white marks are joint compound (aka "drywall mud") - kind of like plaster. The stripes are where separate sheets of drywall are joined with tape and mud and the little splotches are where screw holes have been covered over with mud.
Those actually are good places to install your storage rack because they indicate the locations of the lumber framing that the drywall is hung on. Basically the garage structure is a framework of wooden 2x4 wall studs and 2x6 or larger ceiling joists spaced 16" apart. That gives the garage it's shape and rigidity. The drywall is the finished interior surface that you see, and it's screwed or nailed into the studs.
If you're installing a storage rack, it's really important that you fasten it to the studs, because the drywall itself is only about 1/2" thick and has relatively little strength to hold any heavy load. In a painted wall, it's common to locate studs by knocking to feel solid spots, or using a stud finder tool. In your case though it's easy, because you can see the stud locations by where the drywall is fastened.
There is a stud or joist running behind each seam between drywall panels (long white stripes) and behind each of the parallel lines of screws (little white splotches).
As pointed out in the comments below, the actual studs are only 1 1/2" wide (45mm in metric), and the splotches are a bit wider than that, but you can find the exact location of the studs by looking for little circle marks where the head of the drywall screws are buried. Trace a line through these to find the rough center of the stud. Just center your fasteners for the lumber rack on these lines and you should be good to go.
If you're in doubt about whether you're lined up over a stud, drill a small pilot hole - either you'll break through the drywall into a cavity, or you'll continue drilling into the stud. If you hit a stud, you'll feel continued resistance on the drill and you'll see bits of wood and sawdust come out on the drill bit.
That said, there are exceptions. In my house (1950s era) the ceiling drywall is installed over relatively thin strapping that runs perpendicular to the joists, and it would be unwise to try and support a heavy weight from those straps. If you're hanging something heavy, take precautions to check that the fasteners are secure and the brackets can support the weight. Also, in North America a wooden structure is typical, but in other places the studs might be steel. If anything seems weird, take a pause until you can figure out how the structure works and how to safely fasten to it.