Physical and verbal abuse both occur in a variety of settings, and both have negative long-term effects. Abuse is anything that hurts you, either mentally, physically or emotionally, and is usually carried out by a person in a position of authority. The terms "physical" and "verbal" describe the actual action of abuse. The means of abuse vary dramatically, but the long-term effects from being in an environment where abuse is both carried out and tacitly condoned are very similar.
The hallmark of physical abuse is that it involves violence. Grabbing someone, shaking her, pushing her or hitting her are all forms of physical abuse. The key component of the definition, though, is that it is consistent and leaves the abused in a constant state of fear and reduced self-esteem. Violence is just one way that some people leave others in this state.
Sexual abuse is a form of physical abuse, although it doesn't necessarily have to be violent. If someone carries out any unwanted sexual maneuver on you, this is abuse, regardless of whether it is violent or not. Again, the underlying theme is that the abuse creates a generally negative life for the abused, and sexual abuse is another physical manner in which this can happen.
Verbal abuse is abuse that is carried out with words. It is harder to define because people -- particularly people who are very close to one another -- do have fights, and unkind words are occasionally said. However, it is abuse if it gives the abused person low self-esteem from the constant fear of a verbal tirade against him. The difference between verbal and physical abuse is simply in how it is carried out -- the long-term effects are similar.
Emotional abuse is a wider-ranging definition, but it tends to have more of a verbal component than a physical component. While verbal abuse involves name calling and generally verbal expressions of negative emotions, emotional abuse is this plus a variety of other forms of control and intimidation. It is not uncommon for emotional abuse to involve verbal abuse, economic isolation (by denying you access to money) and strict rules about when you can see other people. So, the difference between verbal and physical abuse in this case is that verbal abuse is usually part of emotional abuse while physical abuse is usually not.