The main difference is in the fact that 7010 is basically a cellulose-sodium, non low hydrogen electrode as is 6010 whereas 7018 is an iron powder, low hydrogen electrode. The alloying will be different as well as other finished surface characteristics and physical/mechanical properties.
The decision for various electrodes will be based upon several factors: tensile/yield strength, notch toughness, alloy content, and many others. The project engineers SHOULD know what they are looking for and smaller diameters are often not as critical as when they start getting larger, thicker, and have more pressure.
Many times on piping, the roots and at least the hot pass if not some fill, are done either with 6010, 7010, or GTAW with the last of the fill or at least the cap being done with 7018.
Only the project engineer really knows why they called it out as they did.
He Is In Control, Have a Great Day, Brent
As Brent said, the difference is really in the type of flux, they are both a 70K tensile rod for all positions.
In my experience (and I have welded with both types of rod extensively) the 7010 was used when welding downhill to the API 1104 code (fill and cap only, root was done with 6010), the 7018 was used for welding uphill to the ASME B31 codes (again, fill and cap only, root was done with 6010 or GTAW).
I've never seen 7010 specified for use in an ASME B31 (uphill only) type application, only for filler and caps on pipeline projects where welding is performed downhill.