To elaborate a little more.
Allowances are payable irrespective of whether the amount paid is actually used for the specific purpose it is meant for. Under normal circumstances, they are fully taxable. However, the Income Tax Act states that some allowances are partially or totally non-taxable, depending on the circumstances - for instance, House Rent Allowance, Conveyance Allowance, Leave Travel Allowance - refer to the ITA for full details on how these can be deemed partially or totally non-taxable.
On the other hand, reimbursements are payments made when a specific payment is incurred and allowed as a tax-free payment subject to certain limits. For example, reimbursement of medical expenses subject to laid-down limits.
The taxability of either an Allowance or a Reimbursement depends on the Income Tax Law then in force. So, you have to do some research to know the exact taxability of any payment made. I hope this has cleared matters.
Jeroo