Not only from a book but also from research into Hindu theology. Oh, excuse me, I also lived in India for 20 years.Still, that doesn't mean that what you know is correct.
You are right, ak, because dharma has a multiple of meanings. When it comes to the caste system, the Laws of Manu apply and basically the common understanding of it among Hindus is following your system.
"The meaning of word “dharma” depends on the context, and its meaning evolved as ideas of Hinduism developed over its long history. In earliest texts and ancient myths of Hinduism, dharma meant cosmic law, the rules that created the universe from chaos, as well as rituals; In later Vedas, Upanishads, Puranas and the Epics, the meaning became refined, richer, complex and the word dharma was applied to diverse contexts. In certain contexts, dharma designates human behaviours considered necessary for order of things in the universe, principles that prevent chaos, behaviours and action necessary to all life in nature, society, family as well as at the individual level.
][note 1] Dharma encompasses ideas such as duty, rights, character, vocation, religion, customs and all behaviour considered appropriate, correct or morally upright.
The antonym of dharma is adharma (Sanskrit: अधर्म), meaning that which is “not dharma”. As with dharma, the word adharma includes and implies many ideas; in common parlance, adharma means that which is against nature, immoral, unethical, wrong or unlawful."
How this relates to karma is maybe a little easier to explain. In the West there are several statements that might be similar to the concept of karma. "Actions have consequences", "birds of a feather flock together" are just two of them. Karma is based on the idea that what you do affects your future. That's why I resisted the use of + - system here. Karma is the worst word for it because the justice that karma effects is not directed by others but by cosmic laws. That's why Kevin responded to you about this.
Just to throw a monkey wrench into the works, here's what WIKI says about karma
"Karma, also refers to a conceptual principle that originated in India, often descriptively called the principle of karma, sometimes as the karma theory or the law of karma. In the context of theory, karma is complex and difficult to define. Different schools of Indologists derive different definitions for the karma concept from ancient Indian texts; their definition is some combination of (1) causality that may be ethical or non-ethical; (2) ethicization, that is good or bad actions have consequences; and (3) rebirth. Other Indologists include in the definition of karma theory that which explains the present circumstances of an individual with reference to his or her actions in past. These actions may be those in a person's current life, or, in some schools of Indian traditions, possibly actions in their past lives; furthermore, the consequences may result in current life, or a person's future lives. The law of karma operates independent of any deity or any process of divine judgment