Got you! That would be the easiest option. And no extra wire needed in that case. Do you have any idea why would the testers show different results ? If I use a multimeter and connect one lead to my hot and the other to the junction box it does reads 120V. So that should mean there is some kind of grounding already?
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You can also do a continuity check between your metal junction box and the neutral feeding the garage. If there is continuity and you're getting 120V between the metal junction and your garage hot, then you're grounded. If you're not sure if your garage feed was done in heavy wall rigid or pvc then you can also do a continuity test between both ends of the pipe. Run a piece of scrap wire (you can wire nut together a bunch of scrap wire, so long as it's a continuous path) from one end (pipe going into garage) of the conduit run to the other end (house feed). Strip your wire and clamp onto the pipe feeding said end (house feed). Test the continuity between the wire and the feeding pipe at the other end (garage feed). If you have continuity then it was done in rigid and you're grounded.
Is the conduit run feeding your garage going directly into the electrical panel or is it tapping into a junction box within your house?
If it is going directly into your panel then as others have stated, you can then change your garage feed into a multiwire branch circuit. In this case you'd need to identify the white neutral wire that will now become your new equipment grounding conductor at both ends (garage and electrical) with green tape.
If you're not sure which neutral it is at either end, you can do a continuity test to make sure you're changing over the correct wire. For this continuity test you can turn off one of the breakers feeding your garage. Unscrew the wire from the breaker. Locate the hot in your garage that you turned off (remember this wire). Turn off the OTHER breaker feeding your garage (there should be no power in your garage). Unscrew your two neutral wires from the neutral bus terminal. In the garage, wire nut together one of the neutral wires and the first hot that you turned off (the one I told you to remember) . In your panel, you should now have 2 loose neutral wires and 1 loose black wire. Check the continuity between the black wire and each of the neutral wires. The neutral wire with the continuity (your meter should beep) is going to be your new equipment grounding conductor that you'll be marking with green tape. If you have a grounding bar (that is bonded to your neutral terminal) in the panel then attach that wire to the grounding bar. Reconnect your other neutral wire.
Since this is now a multiwire branch circuit you'll need a two pole breaker for your two garage hots. Don't turn anything on yet, because you still have to rework your neutrals and grounding conductors in the garage. If your garage is run with EMT and metal junction boxes (double check your locknuts and connectors) then you can bond your new equipment grounding conductor directly to the box and your garage should be grounded. You need to separate your equipment grounding conductor from your neutrals in your garage as well. At the first junction box going into the garage from the electrical panel connect all of your white neutral wires together and bond your new grounding wire to the enclosure. It looks like you have a plastic box for your first junction box, so you'll need to do another continuity test (or pull on it and see which one is moving) to identify the neutral wire that you'll be changing into a grounding wire. Grounding wires spliced together and bonded to your metal enclosure. Neutral wires spliced together and kept separate from the grounds.
IF your garage feed is tapped from a junction box inside your house, then the process is the same. Turn off your garage feed breakers. Identify the neutral that will be converted into a grounding wire at both ends. Label said neutral at both ends with green tape. Bond the new equipment grounding conductor to either the metal junction box enclosure (assuming everything is done in EMT) or splice to your equipment grounding conductors within your junction box (If everything isn't done in EMT). MOST importantly, you must now trace back those neutrals back into your panel and rework them within all the junction boxes associated with those circuits. Don't forget to change the garage circuits to a 2 pole breaker.
Those testers are nice in a pinch and great for testing out the outlets you've installed on a job, but they can be unreliable at times. Especially the cheap commercial electric ones. Your multi-meter is your testing tool for troubleshooting.