These two terms get mixed up because both involve someone illegally affecting a play. The key difference is simple: obstruction is committed by the defence against a runner, while interference is usually committed by the offence or a runner against the defence making a play.
A fielder actively attempting to field a batted ball has priority over a runner, so the runner must avoid hindering that attempt even when the fielder moves into the basepath. That protection normally belongs to the fielder the umpire judges is entitled to make the play; another fielder who is only backing up cannot freely block the runner. Once the ball has passed and the fielding attempt has ended, a fielder without possession must avoid impeding progress. A thrown ball does not give the same broad protection as a batted ball, although a fielder may move into the runner's path while actually possessing the ball for a tag.
If a play is being made on the obstructed runner, or the batter-runner is obstructed before reaching first, the umpire calls time and makes the prescribed award. When no play is being made on that runner, the umpire signals obstruction but lets action continue. After play ends, runners are placed where the umpire believes they would have reached without the violation. That delayed call is why a runner may continue beyond the next base at risk: the protection is based on the umpire's judgment, not an unlimited free advance. Awards can also move other runners when needed to remove the effect of the obstruction.
Runner interference with a fielder attempting a batted ball generally makes the ball dead and the offending runner out. Intent is not always required away from a legally occupied base. Interference designed to prevent a double play can create an additional out. Batter, coach, bench, spectator, and umpire interference each have their own definitions and remedies, so “interference” is a family of rules rather than one universal penalty. Start by naming who interfered, what defensive play was hindered, and whether the contact was intentional where the specific rule requires intent.
A shortstop moving across a runner's path to field a ground ball is normally protected, and a collision caused by the runner can be interference. If the shortstop misses the ball and then remains in the path without possession while the runner tries to advance, the protected fielding opportunity may have ended; the later hindrance can be obstruction. Umpires separate those moments instead of assigning one label to the entire collision sequence.
Contact alone does not decide it. The umpire still has to ask who had the right to that path at that exact moment and whether the fielder was legally making a play on the ball.