If you have DECIDED to do something it implies a DECISION has been made and it will happen. I have decided to learn English (this could change I may learn French instead). If you are determined to do something it implies more of a resolve, your mind will not be changed, you will stop at nothing to make this happen. I am determined to learn English (this definitely will happen) I hope this makes sense :-)

Here is an example: You decided to do something, after you determined it was okay. 'Determine' implies some thought or consideration.

They are both verbs. In your question, "to decide" is the action, we would use it in a narrative. (i.e. he decided to go to the beach today.) As for "determined," in your question it is an adjective, so it mean "willing to complete," usually. We use it more as an adjective than the verb. It is too formal for casual English.

"determined" implies that there was some thinking or consideration and a conclusion arrived at before the decision was made. 希望这个会帮助