What is the difference between moving forward with determination and forging ahead with determination?

Different semantics, different usage, etc.

Different semantics: Forging ahead focuses on the meaning of going through trials and overcoming difficulties, emphasizing the need to experience some difficulties and challenges in the process of moving forward. Moving forward with determination pays more attention to the meaning of invigorating the spirit and moving forward, emphasizing the need to maintain a positive attitude in the process of moving forward.

Different usage: Forge ahead is used to describe the courage and perseverance of an individual or group in the face of difficulties and challenges. Moving forward with determination is used to describe a state in which an individual or group maintains high enthusiasm and firm belief in pursuing goals, actively moving forward, and making continuous progress.