I understand your intentions are pure and you mean well but this is completely wrong and I would like to clear it up a bit for anyone who bothers to read this.

The phrase "common assault" refers to assault and battery together, and this is frequently shortened to "assault".

So on a side note, you know what people mean by "assault", no need to be pedantic.

Furthermore, and this is my main point, you say that battery is "much, much worse". It's really not. It is worse, yes, but not "much" worse. I'm going to explain it in terms of the English court system but it's basically exactly the same in America as your legal system is based on ours.

Assault and battery are both summary offences. That means it's the least serious type of criminal offence. They are both heard in a Magistrates' court so the maximum possible sentence is 6 months for both.

Battery, essentially, is assault combined with ANY touching. Even touching of clothing can be battery (R v Thomas 1985, in which the touching was not even evidently indecent)

Generally injuries inflicted in sport do not merit criminal liability, however in this case the attack was not a part of the game and therefore would.

The only way the assault in the GIF would be charged as more than a battery is if there was any physical injury. Any physical injury that is more than trivial takes it higher than battery. Even moderate bruising is potentially enough.

I won't go into details (unless anyone is interested), but a concussion would be ABH and brain damage would be GBH. The specific type (i.e. section 18 or section 20) would depend on the defendant's intention, they carry very different sentences. If this was on a field and they were wearing studded boots, then a resulting cut could cause it to become GBH provided all layers of the epidermis were broken.

Source: Law student

Edit: As others have pointed out, battery does not require the apprehension of unlawful force whereas assault does. I knew this was the case, but I usually find that assault+touching is an easier way to explain it to get the gist of it. But here's the clarification :)