Hmm in German you could also say "Betriebssicherheit" (safety) vs. "Angriffssicherheit" (security), or at least that always was the translation that made most sense to me personally.
I'd say native speakers of German distinguish it but it depends on the context ... talking about computers, it's typically more about security, while when talking about construction sites, it's typically more about safety.
But they are both "Sicherheit" since in compound words the main word is the last word. You could say "Ist dein Haus sicher?" and mean "is your house secure" if a burglar is targeting your neighbourhood or "is your house safe" if a storm is passing over it. You can distinguish both cases with context or compound words, but it's not generally done.
I'd say native speakers of German distinguish it but it depends on the context ... talking about computers, it's typically more about security, while when talking about construction sites, it's typically more about safety.