You made a journey by train, where the ticket cost $100 and no additional costs arose.
Afterwards somebody (who is in no way liable to give you a cent for the journey) is so kind as to give you some amount of money nevertheless. Consider the following cases:
a. You get $200, because you had all the labour travelling from A to B.
b. You get $100, because that is the sum which you did pay yourself.
c. You get $80, because you probably had some fun travelling, which is rated as $20.
d. You get $10, because more money is not available for this.
(The reasons are just examples. The relation between actual cost and contribution is of greater importance.)
Is this in all four cases called "travel allowance", or what are the correct terms? Although travel allowance is an accounting term, this question is not about accounting. I just do not know the right term for it.