Yup. It's a rig. It can search or reach for oil among other things.

That said, what does exploratory mean in this context?

It means you're drilling a hole and dropping sensors down it to get a better idea of whether a particular location would be profitable to extract oil/gas from. Production platforms are semi-permanent structures that do the extracting once oil/gas have been found. (My knowledge of the field is pretty old but AFAIK, things still work pretty much the same way--although I assume seismic tools locate oil/gas reservoirs without drilling have gotten a lot better.)

I'm sure that's fair. I was in the offshore drilling industry for a few years so I'm more aware of the nuances (at least on the exploratory drilling side) than most.