Offenbar vs. offensichtlich
The German words offenbar and offensichtlich can both be translated as apparently or obviously, but they are not interchangeable. The key difference lies in the level of certainty they express, distinguishing between a strong assumption and an undeniable fact.
Offenbar
B2offenbar means apparently or it seems. It is used when you conclude something based on strong evidence or signs, but there is still a slight possibility that you are wrong. It expresses a high degree of probability, not absolute certainty.
Der Nachbar ist offenbar im Urlaub, der Briefkasten ist voll.
(The neighbor is apparently on vacation, the mailbox is full.)
Sie hat den Job offenbar bekommen, denn sie hat Sekt gekauft.
(She apparently got the job, because she bought sparkling wine.)
Er hat offenbar den Bus verpasst, deshalb kommt er zu spät.
(He apparently missed the bus, that's why he is late.)
Die Pflanze ist offenbar eingegangen, sie hat alle Blätter verloren.
(The plant has apparently died, it has lost all its leaves.)
Jemand hat hier offenbar sein Portemonnaie vergessen.
(Someone has apparently forgotten their wallet here.)
Offensichtlich
B1offensichtlich means obviously or evidently. It is used for things that are plain to see, directly observable, or proven without a doubt. It expresses certainty based on clear, undeniable facts.
Es regnet draußen, die Straße ist offensichtlich nass.
(It's raining outside, the street is obviously wet.)
Mit Tränen in den Augen war sie offensichtlich traurig.
(With tears in her eyes, she was obviously sad.)
Zwei plus zwei ist offensichtlich vier.
(Two plus two is obviously four.)
Er trägt einen Gips, sein Arm ist offensichtlich gebrochen.
(He is wearing a cast, his arm is obviously broken.)
Der Fehler in der Rechnung ist offensichtlich, wenn man genau hinsieht.
(The mistake in the calculation is obvious if you look closely.)
Summary
In short, use offensichtlich when something is a clear, undeniable fact that you can see or prove directly (obviously). Use offenbar when you are making a very strong and logical assumption based on available evidence, but you cannot be 100% certain (apparently). offensichtlich relates to objective proof, while offenbar relates to a subjective but well-founded conclusion.