When would an 'unlawful' touching be a sexual battery?
The answer to this depends to a great extent on the jurisdiction you are asking about. This is because there is not necessarily a crime called "sexual battery" that is distinct from regular battery.
If you look at the definition of battery, it covers any offensive touching. As the West's Law Encyclopedia link below puts it (I added the bold print)
The second type of contact that may constitute battery causes no actual physical harm but is, instead, offensive or insulting to the victim. Examples include spitting in someone's face or offensively touching someone against his or her will.
Therefore, by definition, any unwanted touching of another person's private parts would be a battery.
However, many states do have separate laws against sexual battery. For example, as seen in the shouselaw.com link, C
California Penal Code Section 243.4 (e) (1) defines misdemeanor sexual battery as the non-consensual touching of the intimate part of another for (1) sexual arousal, (2) sexual gratification, or (3) sexual abuse.
Thus, by this definition, sexual battery involves a speficic type of intent -- the intent to gain sexual gratification or the intent to sexually abuse -- that is different from what is required to prove regular battery.
As the term implies, any touching of a person in a sexual manner if the touching is uninvited, unwanted, or the person is under age constitutes a sexual battery. The actual touching itself is a battery. It is rises to the level of sexual battery if the touching has sexual overtones. If one touches another's genitals or a woman's bosom, then one is guilty of sexual battery. One is inclined to construe sexual battery to constitute rape; but it is only an extreme form of sexual battery. One only need make physical contact. It is normally anticipated that the touching is a prelude to the more pernicious act of rape; but one may have been prevented from proceeding further.