" 褐色”is a little bit darker than " 棕色”. Generally , we can also say " 黑褐色“ or "红棕色". So from these two words you can know what they are like.
The two colors are very similar. We don't really know what the color is if you say either of them, because we may have slightly different definitions of them according to our own educations or experiences. Normally, people will ask you for more details if you need to be very sure.
Actually you will also come across " 红褐色”，“棕褐色”or " 黑棕色“. All these color names are very confusing. Just ask or explain more when necessary.