The amount of time the adhesive should be left to set, before it is covered.
If you're gluing two sticks together, with an adhesive with 30 seconds open time. You should apply the glue to one stick, then wait at least 30 seconds before affixing the second stick.
The amount of time the adhesive can be left before it is covered.
If you're gluing two sticks together, with an adhesive with 30 seconds open time. You should apply the glue to one stick, and affix the second stick before 30 seconds has elapsed.
The amount of time from when the adhesive has set, to the time it will no longer bond.
Again gluing two sticks together, this time with an adhesive with a 5 minute working time. Once you apply the glue to the first stick, you have to affix and position the second stick in less than 5 minutes. If you don't affix the sticks within this time, the adhesive will not bond (or at least is not guaranteed to bond).
The amount of time the adhesive needs to form a good bond.
Back to the sticks, this time with an adhesive with a 10 minute set time. Now that the sticks are affixed, you'll have to wait 10 minutes before they are adequately stuck together.
The amount of time an adhesive can remain viable after being mixed.
If you're gluing the sticks using a 2 part epoxy, with a pot life of 2 hours. Once you mix the epoxy, you have 2 hours to use it before it becomes useless.
*Some manufacturers use open time, and working time interchangeably. Open time should only be assumed to be different than working time, when working with adhesives that need to activate or set before being usable.
After doing more research, it appears there really isn't a set vocabulary used throughout the industry. Your best bet would be to contact the manufacturer, and ask them what they mean.