Here's another take, from a "former future" engineer.  Conservation means using less of a resource, through whatever means.  Efficiency is how much of a resource you use in achieving some result.  So it's through large increases in efficiency that a Ford Explorer gets the same gas mileage as a Model T, but there is no conservation involved, since they have the same gas mileage.  Worse, there was extra consumption involved, since the person using the Model T would never have considered driving it as much as people drive today.

So, efficiency can, but does not necessarily, lead to reduced consumption, but conservation requires a reduction in consumption.  Note that you can use efficiency gains to do more with less, in which case you are both increasing efficiency and conserving.  New refrigerators compared to old fall in this category; the increase in efficiency is so significant that you can have a bigger fridge that also uses less electrity.  Except for the perceived loss of status, you can get a similar effect switching between an SUV and a gas-sipper, since most SUVs aren't used to carry any more than a small sedan could carry.

You can also conserve without changing efficiency or even while reducing efficiency, by just using something less or not at all.