Basic Allowance for Housing (BAH) and Basic Allowance for Quarters (BAQ) are both military allowances designed to help offset the cost of housing expenses for military service members. However, there are some key differences between the two allowances. While they technically mean the same since they are an allowance for service members for housing facility, the only difference is that BAQ is the previous version of BAH and BAQ mostly paid for government quarters. This means BAQ or allowances for quarters is no longer a valid term and only the BAH term is used in the military now.