I'm somewhat new to using logistic regression, and a bit confused by a discrepancy between  my interpretations of the following values which I thought would be the same: 

 - exponentiated beta values 
 - predicted probability of the outcome using beta values. 

Here is a simplified version of the model I am using, where undernutrition and insurance are both binary, and wealth is continuous:

    Under.Nutrition ~ insurance + wealth

My (actual) model returns an exponentiated beta value of .8 for insurance, which I would interpret as:

> "The probability of being undernourished for an insured individual is .8 times the probability of being undernourished for an uninsured individual."

However, when I calculate the difference in probabilities for individuals by putting in values of 0 and 1 into the insurance variable and the mean value for wealth, the difference in undernutrition is only .04. That is calculated as follows: 

    Probability Undernourished = exp(β0 + β1*Insurance + β2*Wealth) /
                                 (1+exp(β0 + β1*Insurance + β2*wealth))

I would really appreciate it if someone could explain why these values are different, and what a better interpretation (particularly for the second value) might be. 



********** Further Clarification Edits ************
As I understand it, the probability of being under-nourished for an uninsured person (where B1 corresponds to insurance) is:

    Prob(Unins) = exp(β0 + β1*0 + β2*Wealth) /
                                 (1+exp(β0 + β1*0+ β2*wealth))

While the Probability of being under-nourished for an insured person is:

    Prob(Ins)= exp(β0 + β1*1 + β2*Wealth) /
                                 (1+exp(β0 + β1*1+ β2*wealth))

The odds of being undernourished for an uninsured person compared to an insured person is:

    exp(B1)

Is there a way to translate between these values (mathematically)? I'm still a bit confused by this equation (where I should probably be a different value on the RHS):

    Prob(Ins) - Prob(Unins) != exp(B)

In lam-en's terms, the question is why doesn't insuring an individual change their probability of being under-nourished as much as the odds ratio indicates it does?  In my data, Prob(Ins) - Prob(Unins) = .04, where the exponentiated beta value is .8 (so why is the difference not .2?)