Variance of WTI Texas crude price Mar 20 2020

If you are referring to futures contracts, then there are some things to consider:

There are more than one futures contract. They are offered by different exchanges - most notably, theICE and CME. They are not the same, they are not fungible, but for most casual observers they offer an easy way to see the 'ballpark' value of Oil.

Its not useful to consider the concept of a 'close' price for futures contracts. A much more useful concept is the settlement price. This is the price that is used to mark to market all the open positions, and as such is sampled / produced in a rigorous way so that it represents an accurate valuation of the contract for that day.

However note that, different contracts may have different settlement price methodologies, and may for example sample the market at different points in the day, so they are not directly comparable.

If you want to use a stream of prices that represents a consistent valuation of Oil, then I would recommend the settlement price of the first WTI future traded on the CME as that is highly liquid.

I would only use the CME website or repuatble feed of the CME data (eg, Bloomberg etc) as a source for these values. Intermediate websites like businessinsider.com etc can, have and will made mistakes. When sourcing market data, always try to cut out the middle man as much as is possible / practical as that eliminates sources of error.

Looking at the website you reference, it doesn't even state whether the values are from the futures contract market, or the spot market. That's a red flag right there, that they don't specifiy. The discrepancy could be that one website is showing the spot price, and the other a futures contract. Unless they give exact details, then its impossible to know for sure.