depending on; in accordance with; according to
Used after a noun or noun phrase to indicate that something changes or is decided based on that factor. Often used in formal or explanatory contexts.
The fee varies depending on the time.
Please adjust your response according to the situation.
に応じて means 'depending on' or 'in response to' and focuses on a matching or adaptive relationship, whereas に従って focuses on a proportional or sequential change as another thing progresses.
From the verb 応じる (to respond, to comply) in its te-form, used as a compound particle meaning 'in response to' or 'according to'.