I think for Assistente de Contabilidade "Accounting assistant" would do.

https://www.serta.apply2jobs.com/ProfExt/index.cfm?fuseaction=mExternal.showJob&RID=2124&CurrentPage=1

    For Auxiliar de Contabilidade, I would  say "Junior Accountant" would fit well , considering the guy/girl is in his apprenticeship (I think).

    In general, both could be used in most contexts with no big difference in sense.

    Let´s wait more answers/comments.