The tray the motherboard is mounted on should be grounded, and motherboard screw holes that have a silver coloured ground pad round them should be screwed down to a metal standoff pillar so those screws should be grounded. However paint is an insulator so it is likely your PSU doesn't ground properly to the case. Fortunately the 0V wiring coming from the PSU and going to the motherboard and drives is normally internally grounded in the PSU and that will be grounding your motherboard. Check continuity between the PSU screw you tested to earlier, and a black wire on a spare drive power connector (old style connector not SATA power connector) to confirm that.
Fixing your PC's internal chassis grounding problems could be quite tedious. It will probably involve a lot of work scraping away tiny circles of paint under screw heads, and/or fitting serrated washers under the screw heads.
I wouldn't trust there not to be a potential difference between two outlet grounds unless they are on the same faceplate or power strip. However ESD grounding almost invariably has high value series resistors, and potential differences in grounding systems are typically very small, so with no low impedance path between the two grounding plugs other than the ground wiring in the wall, there are no significant risks to you or to equipment. Before putting multiple grounding plugs into service, plug them in and check the resistance between their ESD grounding connectors is double that between a single plug's ESD grounding connector and its ground pin. If there is no resistance between the connector and the pin you *MUST* use ESD leads with a built-in safety resistor.
Whether or not your outlets are grounded at all or to the same ground can only be definitely resolved by resistance measurements with the breaker(s) in the panel feeding them off, between them, and a ground point in the panel and a temporary test ground rod. Doing such tests properly requires a good working knowledge of your electrical regulations (US National Electrical Code), and specialised test equipment which is why calling a qualified electrician is recommended if you don't have previous experience and training in performing NEC compliant electrical work. A rough check can be made with an ordinary multimeter, but if there is a pre-existing fault, dangerous voltages may be present on supposed grounds so be careful and test for voltage difference before doing any resistance checks. A socket tester is useful as a quick and cheap check that anyone can make that shows you if Line, Neutral and Ground are present at a socket and wired to the correct pins, but it wont find connections that have a higher than normal resistance e.g. due to a loose terminal screw, wirenut or backstab connector + oxidisation on the wire end.