安全 and 安心: safe conditions and peace of mind
Distinguish safe conditions from reduced worry, recognizing that feeling reassured does not itself establish safety.
Assess a condition
安全な場所で待ってください。 asks someone to wait in a safe place. 安全, read あんぜん, concerns whether a situation is free of danger or poses little risk.
作業の前に安全を確認しました。 says that safety was checked before work. The sentence alone does not specify what was checked.
Worry subsides
無事に着いたと聞いて、安心しました。 says that someone felt relieved on hearing of a safe arrival. 安心, read あんしん, describes the emotional response of being reassured.
説明を聞いたので、安心して申し込めました。 says that hearing the explanation enabled the speaker to apply with peace of mind. It includes both reassurance and being able to apply.
Keep feeling and conditions distinct
本人は安心していますが、安全かどうかはまだ確認していません。 says that the person feels reassured, but safety has not yet been checked. The two judgments can rest on different grounds.
安全な道 describes a safe road; 安心して歩ける道 describes one a person can walk along without worry. Distinguish a condition from the user's state of mind.
Does 安心しました mean that every risk has been checked and removed?
Show the answer and why
No. It means that worry subsided and the person felt reassured. The extent of any actual safety checks needs separate information.