How are positive and negative feedback of opamps so different? How to analyse a circuit where both are present?

In an opamp, feedback on the positive input places it in saturation mode and the output is of the same sign as V+ - V-; feedback on the negative input places it in "regulator mode" and ideally Vout is such that V+ = V-.

1. How does the opamp change its behaviour depending on the feedback? Is it part of a more general "behavioral law"? [Edit: Isn't it something in the lines of the voltage added increases the error instead of reducing it in the case of + feedback?]
2. How can we analyse circuits where both are present?

Whoever answers both at the same time in a coherent manner wins a pot of votes.