Both these buses are the X2 service connecting Oxford and Didcot via Abingdon, but the company and livery have changed in the last two weeks.
The X2 used to be run by the Red Oxford Bus Company based in Oxford, but is now run by the Blue Thames Travel based in Wallingford.
Thames Travel were bought by the Go Ahead Group in May 2011, which brought it under the management of the Oxford Bus Company which the Go Ahead Group bought in 1994.
It means that both the X2 and the 32 Oxford-Abingdon-Didcot services are run by Thames Travel. The main difference between these services, if any visitor asks, is that the X2 stops in South Abingdon and goes that way round, and the 32 stops on Bridge Street and goes that way round.
There is an X32 but it goes direct from Oxford to Didcot missing Abingdon. Do not make that mistake!