Housing Allowance and Parsonage, Are they the same?
No. A parsonage is simply a place where the minster and his family live. It is owned by the church.
A housing allowance (or parsonage allowance) is a special benefit that ordained ministers receive income tax free.
IRC section 107 permits qualified ministers to exclude housing-related compensation from gross income to the extent it relates to service performed in their ministry.
In plain English: Ministers who own or rent their homes or live in a church provided parsonage may be able to exclude from their federal income taxes a portion of their salary that has been designated by their employer as a "housing" allowance.
The housing allowance is sometimes called a “parsonage allowance” for minister who are provided with a parsonage and a “rental allowance” for ministers who rent their home.
***Note: Even though a housing allowance is excluded from a minister’s federal income tax, it is not excluded when figuring his self-employment tax. (taken from the ebook Housing Allowance)