Acknowledge usually refers to some sort of PHYSICAL action used to express that you have seen or heard somebody. Example: “He acknowledged what she said by nodding his head.” “When she saw him at the party, she would not even acknowledge that he was there.” Recognize usually refers to a MENTAL state of looking at something or someone and knowing what or who it is. Examples: “I don’t recognize anyone in this photograph.” “I haven’t seen her for 10 years, and when I saw her today at first I didn’t recognize her. She has changed so much.” “I can recognize over 1000 Chinese characters.” There are other uses of acknowledge and recognize, but I hope this helps.

They are words that are somewhat hard to define without being in terms of each other. to recognize means to be a person that learns/remembers information while to acknowledge means to recognize the person/information that has been learned. (they are somewhat connected like a cause and effect relationship if that helps).