Both words involve the eyes and the power of vision. You can both ‘look at’ something and ‘see’ something with your eyes. The words are considered synonyms for each other, however, there is a difference in the meaning and usage of the words.
‘Look’ when used as a verb can transitive or intransitive, so it can be used with or without an object grammatically. It means to direct the eyes and attention in a particular direction, but especially to examine or search for something with the eyes. For example: She looked at the ocean all afternoon. It can be used as a command to focus the eyes on something. For example: Look what I have for you here! Along with this definition, it can take on the meaning to stare or gaze at in wonder or surprise. For example: He just looked at me when I showed up early. ‘Look’ can also have a more abstract meaning of expecting or anticipating something. For example: We are looking forward to your visit. As well, it can refer to the appearance of something or its expression. For example: She has the look of an educated person. Finally related to the verb meaning, ‘look’ can be used as a noun to mean the act of looking at, examining, trying to find or considering something