警戒 and 恐怖: vigilance and the feeling of fear
Compare precautions toward danger cues with fear of a scream or failure. Keep increased vigilance, overcoming fear, and the actual assessment of a danger separate.
Paying attention to a possible danger
警戒（けいかい） means vigilance or caution. 山では野生動物に警戒しながら歩いた。 describes walking through the mountains while watching for wildlife. 警戒しながら gives the precaution taken while walking.
店員は不審な電話に警戒を強めた。 says that the clerk increased vigilance against suspicious calls. The stronger precaution does not establish that the calls were an actual crime.
What causes fear and what follows it
恐怖（きょうふ） means fear or terror. 暗い森で聞いた叫び声に恐怖を感じた。 describes feeling fear at a scream heard in a dark forest.
失敗への恐怖を乗り越えて舞台に立った。 says that the speaker overcame a fear of failure and went onstage. It gives that action, without establishing the later success of the performance.
A precaution and an emotion can overlap
Someone who is vigilant may also feel fear, and someone may take precautions without feeling fear. The words are neither necessarily simultaneous nor mutually exclusive.
警戒を強めた states that vigilance increased. It does not by itself show that fear increased or that the danger disappeared. Identify the danger cue separately from any emotion described.
Does 店員は不審な電話に警戒を強めた。 establish that the clerk became more afraid?
Show the answer and why
No. It states an increase in vigilance toward suspicious calls. It does not describe a change in fear or determine whether the calls were a crime.