There are.. I believe you want SAE30 or SAE40 oil for direct drive compressors. SAE40 is the thicker/more viscous of the two. Thinner oils have a water-like consistency and pour more easily at low temperatures than heavier, thicker oils that have a more honey-like consistency. Thin is good for easier cold weather starting and reducing friction, while thick is better for maintaining film strength and oil pressure at high temperatures and loads.
The 'Compressor Oil' you can buy in the shops is almost certainly all SAE30... Air Tool Oil is very thin/runny, probably something like SAE10