LadyCG and Waterboatman are both way off the mark.
'Assault by beating' is simply an alternative wording to 'common assault'. It's still a 'Section 39 offence' and carries exactly the same penalties. The wording is used when a 'battery' has occurred but both the terms 'beating' and 'battery' can be severely misleading to someone who's unfamiliar with legal terminology. There does NOT have to be any physical injury suffered by the victim and, even if there is, it would need to be VERY MINOR for the offence to be fall under Section 39. Simply giving someone a slight push, or spitting at them, counts as 'assault by beating'.
While the courts are potentially likely to regard a Section 39 offence against a vulnerable person (such as a child) more seriously than one against a 'non-vulnerable' adult, there is no specific charge in law of 'assaulting a child'. It's still 'common assault' (or 'assault by beating', as appropriate) if the physical injuries sustained are either non-existent or very minor.
https://www.sentencingcouncil.org.uk/blog/post/assault-offences-explained/