Muti meter says +24v but was wondering if that was just the difference between the two points
That's the very concept of voltage: a potential difference. Your multimeter will always indicate the voltage difference between two points.
You can take one of the points as a reference and attribute 0 volts to it.
In the picture below I show the output of your ACDC conv. Notice that the potential difference is the same in all three configurations. What changes is the 0V reference that I can arbitrarily choose.

So you can merrily connect your ACDC conv like in the picture below: +12V to the positive terminal, -12V to the negative terminal of your load, and 0V not connected.

However, there is a caveat. If for some whim of fate the conv and the load get connected by an alternate route, say, some ground provided by another cable connected to the conv and the load, or by a metallic shelf, or the chassis of a car, you're in for a disaster.

How can you be certain that there won't be a problem? Before you connect and turn everything on, use your ohmmeter to test the terminals between the devices for continuity. Test terminal by terminal inverting the leads, because ohmmeters have polarity.

If you're still not sure how to proceed, summon a friend that is acquainted with electricity. Everyone should have such a friend, by the way.