This is a good question. I would say that texting or any type of communication varies depending on with whom we are communicating for several reasons.
First, some relations require more formal or less formal communication. For example, if you text your sister you may be more informal than when texting your grandmother, who requires more formal texting. If you do not know a relation well, that texting will be more formal. If you know a relation very well, your communication will be less formal. For example, a distant uncle and a close uncle will require more and less formal texting, respectively.
Second, age also makes a difference. As a general rule of thumb, there ought to be more respect shown to older people. Moreover, from a practical point of view, older people may not know the shorthand of many young people, especially in the medium of texting. For example, many people might not know things like LOL. For this reason, texting will look different.
These two examples should get you started.