How precedent works
Courts decide like cases alike, that's stare decisis. But a decision's weight depends entirely on where the deciding court sits in the hierarchy.
Binding (mandatory) authority runs vertically
A court must follow the courts above it in its own line of appeal. The Supreme Court binds every court in the country. A U.S. court of appeals binds the district courts within its circuit, and only within its circuit. A district court binds no one but must follow its circuit and the Supreme Court.
Horizontal precedent, a court following itself
Courts also tend to follow their own past decisions. A three-judge circuit panel is bound by an earlier panel of the same circuit unless the full court reconsiders the question sitting 'en banc.' The Supreme Court may overrule its own precedent, but does so rarely and only with strong justification.
Persuasive authority is everything else
Decisions that aren't binding can still be considered: a sister circuit's ruling, another state's high court, a trial court, or the non-essential reasoning ('dicta') in an opinion. A Ninth Circuit holding is only persuasive in the Fifth Circuit, judges there may find it convincing, but they are free to disagree.
Circuit splits and why the Supreme Court steps in
Because each circuit binds only itself, two circuits can read the same federal statute differently. The law then genuinely differs by region, a 'circuit split.' Resolving these splits is one of the main reasons the Supreme Court grants certiorari and takes a case.