What’s the difference between a plugin, observer, and rewrite — does it matter?

Yes, hugely. Quick rule of thumb:

• Plugin — intercepts a public method (before/around/after). Magento’s preferred extensibility mechanism. Multiple plugins can stack cleanly. Use this first.
• Observer — reacts to dispatched events. Use when Magento explicitly fires an event for what you need.
• Preference (rewrite) — replaces a class entirely. Last resort: only one preference per class wins, breaks other modules trying to do the same. We avoid this unless absolutely necessary.

Bad extensions abuse rewrites; good ones use plugins + observers. We default to plugins because they survive Magento upgrades.