Proceed as in to go forward with something or start or continue an action. Example: Despite the cold weather, we proceeded with the tour. Or Proceed to the nearest exit.

Process - as in the order in which a task is done . Or a series of tasks to bring a certian end result Example: Getting old is part of life's process. Or Example: I was processed through flight security and boarded shortly

Process is a noun, while proceed is a verb. Proceed can mean to move forward, as in "Proceed to the nearest exit." Process can mean a series of steps as in "Learning is a process that takes time and patience."