Many states look at assault and battery as two related, but very different, legal charges. The main issue is that an assault can just be a threat of physical violence, while battery is the carrying out of that physical action.
In Texas, they both fall under the general classification of assault. It can be a threat or a physical assault. There are very different ramifications — you could see jail time for a physical assault and merely get a fine for a threat, for instance — but they both count as assault of one variety or another.
That does not mean that all instances are the same, not by any means. The charges can get upgraded to reflect the circumstances.
For example, if you use a weapon while injuring someone else, that can count as aggravated assault. Even if you do not use a weapon, you can get aggravated assault charges for causing serious injuries.
Another specification to be aware of is that you can get assault charges if you threaten someone else’s spouse under Texas law. If they believe they are at risk of imminent physical harm due to what you said and how you acted toward them, you could be charged. If your actions result in a fight between the two of you, they may also use this interaction to show that the fight was your fault.
Since Texas law is slightly different than the law in other states, it is very important to understand these differences and all of the legal defense options that you have when accused of a crime.