In some datasets, income cannot be distinguished from total consumption, usually due to limitations in the survey questionnaire. It is the case in the Argentine Household Expenditure Survey, where total income is not surveyed, but total expenditure is. If one can safely assume savings away, then the two concepts become equivalent so that income and expenditure elasticity are very much the same thing. However, bear in mind the consequences of such an assumption: it implies a zero net financial position for households, an extremely unrealistic situation in a model with macroeconomic implications for example.

Basically  because of budget constraint we assume that total expenditure/ total consumption equals to income.   However, you can also seperately measure income or wealth elasticistes depends on your model. (e.g. using instrument variable) 

As per theories are concerned in  micro economics consumption elasticity and income elasticity are used as analogous. in some cases they may be distinguished regarding a single commodity elasticity and the income elasticity of demand for the whole basket of goods. in the same sense there may be a difference between consumption elasticity for a particular good and consumption elasticity for the whole basket of an individual.