'Assault' and 'battery' are simply different wordings of the same charge. See here for the guidelines that the CPS use when determining the wording in any particular case:
http://www.cps.gov.uk..._the_person/#P92_3540
Both 'assault' and 'battery' are regarded as 'serious' offences by the SIA. See pages 63 and 64 here:
http://www.cps.gov.uk..._the_person/#P92_3540
Page 44 of that document shows that the SIA's policy (where an applicant has committed a single serious offence) is to automatically refuse a licence for a period of two years after the end of sentence restrictions. For the following three years the SIA will consider additional factors before deciding whether to grant a licence. To be sure of getting a licence you must wait until 5 YEARS have elapsed since the end of any sentence restrictions.
Chris