From "Principles of biochemistry", Horton and al, 1993.
Caffeine is sometimes called "theine" when it's in tea. This is probably due to an ancient misconception that the active constituent is different. Theophylline is present only in trace amounts. It is more diuretic, more toxic and less speedy.
Coffee and tea contain caffeine and theophylline, respectively, which are methylated purine derivatives that inhibit cAMP phosphodiesterase. In the presence of these inhibitors, the effects of cAMP, and thus the stimulatory effects of the hormones that lead to its production, are prolonged and intensified.
Theobromine and theophylline are two dimethylxanthines that have two rather than three methyl groups. Theobromine is considerably weaker than caffeine and theophylline, having about one tenth the stimulating effect of either.
Theobromine is found in cocoa products, tea (only in very small amounts) and kola nuts, but is not found in coffee. In cocoa, its concentration is generally about 7 times as great as caffeine. Although, caffeine is relatively scarce in cocoa, its mainly because of theobromine that cocoa is "stimulating".
Theophylline is found in very small amounts in tea, but has a stronger effect on the heart and breathing than caffeine. For this reason it is often the drug of choice in home remedies for treating asthma bronchitis and emphysema. The theophylline found in medicine is made from extracts from coffee or tea.