In common everyday usage, expense and expenditure are used synonymously. Even some accountants use them interchangeably. In the United States tax code, there is a subtle but important difference. No, even though one of my careers is a professional tax preparer, I am not turning this blog into a detailed discussion of taxes. However, the distinction between expense and expenditure is a critical one for any discussion of sustainable economics, especially from the top of Hubbert's Mesa.
To put it simply, an expense is spending money for something which you completely benefit from in the current year; an expenditure is spending money for something which you benefit from for multiple years. For example, your car is an expenditure (or at least I hope if you're reading this blog, you're not buying a new car every year!), the gasoline to fill it is an expense.
Where this distinction relates to sustainability and Peak Oil is that it doesn't just apply to money. For those purposes, though, one year is very arbitrary; it probably should be expanded. For example, making concrete takes a tremendous amount of energy, invariably from fossil fuels these days. If you make concrete objects so that they are only put to one use and then discarded, that represents a substantial energy expense. On the other hand, concrete objects that are designed to be reused over and over are an expenditure that can pay dividends for centuries.
We need to carefully analyze whether the resources we use are expenses or expenditures, because on the Long Ascent, expenses weigh us down, but expenditures are what allow us to go higher.