Once upon a time these two phrases used to be different from each other. But because people forgot or didn’t know the difference, the line that had separated the two has blurred.
Now, American English freely uses one or the other. The New Oxford American Dictionary and Learners Dictionary provide:
On (also in) behalf of and On someone’s behalf
- In the interests of a person, group, or principle. Example: They didn’t consider the votes cast by the labor unions on behalf of their members.
- As a representative of. Examples: He had to attend the funeral on Mama’s behalf. The teacher accepted the award on behalf of the whole class.
- On the part of; done by. Example: This wasn’t simply a philanthropic gesture on his behalf.
Advanced Oxford American Dictionary, however, distinguishes between the two phrases: