What is the drug ether?
Diethyl Ether, more commenly known as Ether was one of the first anesthetics, and was marketed in the 19th century (mixed with ethanol) as a cure-all and recreational drug. It may also be used as an inhalant and can be used to make a variety of illegal drugs such as cocaine and meth. The effects are like drinking vast amounts of alcohol.
From my knowledge, any drug would show up on a drug test. But it depends on how long you took it before the drug test. The best thing to do is to just not take drugs unless they are prescription, and if they are, carry the receipt with you when you go to get the drug test so that you don't create trouble for yourself and others.
Petroleum ether (or pet ether as it's commonly called) does not have any particular chemical formula. All you can be relatively sure of is that there are ethers in it. There could be diethyl ether, butylpropyl ether, dipentyl ether... Pet ether is a solvent, and as such it's not necessary to know its chemical formula. It's simply a medium, not a reactant.