Common factor is that both are Energy sector commodities. One more common factor is, in MCX, price of both will be impacted similarly with INR appreciation/ depreciation.
Apart from these two similarities, I don’t think there is anything common between them. Based on news or fundamentals, sometimes both commodities may head in the same direction. Likewise, both may head in opposite directions based on some other news. Generalising the inter relation between prices of these two commodities will do more of a negative impact on trading than doing a positive impact.
Both the commodities are very sensitive to those news, which indicate modest to high change in demand and supply.
Just to add, logically speaking both energy stocks should move in the same direction. However crude oil has a demand all across the world while natural gas is restricted to US and a few other countries. Hence the demand supply of the world impacts the movement of crude but for natural gas the demand and supply in US is what that matters. Hence both will not trade in the same direction.