3 wire service to older building doesnt look correct
First part is answered here: sub panel bonding. But in short, sub panels are not allowed to have their neutral bonded to ground. That only happens in the main panel.

Now to answer your grounding question: Yes, your sub panel is not properly grounded. Any fault current would have to travel through the earth back to the main ground rod or whatever grounded metal object is in the path first. The resistance of the earth varies and corrosion can also add resistance. This can create a high resistance enabling a ground fault (short to ground) to energize the garages ground circuit with a potentially fatal current without tripping a circuit breaker. In plain English: a short to ground could make every grounded metal object in that building live with respect to the main ground rod. A separate ground conductor must be ran from the main panel ground bar to the sub panel ground bar. That ground wire must also be in the same conduit as the other three feeder conductors and appropriately sized to the hot conductors.