I almost always agree with isherwood, but in this case, my take is a little different.
Diagonal cracks at the corners of doors or windows is characteristic of settlement due to doors and windows having double framing, which makes them strong spots. The question is whether the settlement is old or new. Even if it is old, cracks don't open unless things are moving or under stress.
The texture finish is the kind of thing someone might do to hide repairs, so this could be an old problem. If they just skimmed an old crack without taping it, vibration from trucks going by or the garage door opening and closing could break up the old repair. The lower drywall crack looks wider than just a hairline, though. I wouldn't expect an old repair to open up that much.
The stucco crack would worry me more. It isn't as easy to crack as drywall, and it's hard to make invisible repairs. If it was previously repaired, you are likely to be able to see it if you look for it around the crack. That's less likely to be an old problem with a disintegrated repair.
Even if this is an old problem, that's only relevant if it was initial settlement that is now stable. To me, the signs seem more likely to be an active problem. I would expose the slab along the cracked area. You don't need to go all the way to the footer, just enough to see what's going on in the area. Look at how continuous and level the top edge is, and how serious any cracks are. Use your judgment as to whether it would be prudent to have an expert look at it. You could also post pictures of the stucco cracks and slab here.
Best Answer
There are 2 types of concrete, concrete that cracks and concrete that hasn't cracked yet. Houses are essentially floating on dirt and with proper preparation you can minimize the likelihood of a slab cracking. From the picture it does look like a large crack if it happened all of a sudden and is heaving it may cause an issue due being unlevel/trip hazard. But in general cracks in slabs are pretty common. Sidewalks don't crack often because of the expansion joints in between each section of sidewalk but that's impractical for a basement or garage slab. If it's a new build it may be cause for conren or if your house is an area subject to landslides or the sort, you may want to have someone investigate it.