修正 and 改善: revising a part or improving a condition
Separate what was revised from the improvement sought, and distinguish completed revisions from evidence of their effect.
Revising or adjusting a specific part
修正, read しゅうせい, means revising or adjusting content or form. 原稿の最後の文を修正しました。 means that the final sentence of the draft was revised.
計画を修正する必要があります。 says that the plan needs revision. 修正 can refer to adjusting a plan, not only correcting typographical errors.
Making a condition or method better
改善, read かいぜん, means improving an unsatisfactory condition or method. 待ち時間を短くして、サービスを改善しました。 says that service was improved by reducing waiting time.
使いやすさを改善するために、画面を修正しました。 makes better usability the aim and revising the screen the method. The two words can describe different aspects of the same work.
Checking the action and its effect separately
修正は終わりましたが、効果はまだ確認していません。 says that the revisions are finished but their effect has not yet been checked. Separate the change from verification of its result.
改善が必要です。 means that improvement is needed. It does not report an already improved condition, so distinguish 必要です from 改善しました.
Does 画面を修正しました。 establish that users now find the screen easier to use?
Show the answer and why
No. It states that the screen was revised. Whether usability actually improved must be checked separately.