Here is some history of each:
Chalet: Wooden dwellings with a sloping roof and widely overhanging eaves, common in Switzerland and other alpine regions. The word Chalet comes from the Franco-Provencal speaking area of Switzerland. It was originally used as a term for the home of cattle herders. The herders would bring their cattle from the valleys to the higher altitude regions during the warmer times of the year. The herders lived in the chalets during these times and worked to make cheese and butter (a method which preserved the milk). Just before winter would approach, the herders took their cattle and dairy products back to the valleys. Today, the term chalet is used by the hotel/motel industry as a reference for detached cottages. They often have self contained cooking facilities and bathrooms. They are often located near ski or mountain recreation areas. They can also be found along coastal regions as "weekenders".
Cottage: The term means "dweller of a cotter". In older times they usually housed farmers and herders as a normal residence; mostly for peasants. They were small and quaint, but sometimes included the primary farm house, barn, yard, and overall living and farming area of the property. They often had a half story above the first level which had a window and required maneuvering through the rafters to get around. Later in the 18th century, this term came to also be associated with the homes of weavers and miners. In modern days, cottages are typically referred to as weekend and summer getaways. They are also referred to as cabins in some areas as most cottages in certain regions are constructed of logs.
Cabin: Typically this is a simple dwelling made of logs. In the US at about 1640, log cabins were first constructed by the Swedish in Pennsylvania. Most of the cabins were not intended as permanent homes. Cabins were usually built in locations that allowed for ample sunlight, drainage, and management of frontier farmland. Cabin sizes were mostly based on the distance logs had to be transported, types of trees nearby, and the amount of building time allowed during the warmer season to ensure an adequate shelter was in place for the winter. Cabins became very elaborate in the mid 18th century. The Adirondack style cabins are what many US Park Service lodges used in the early 20th century. Today, many retreats, camp ground facilities, and upscale homes are built using logs. Here is a website showing a history of log cabins in the US:
www.cr.nps.gov/hps/tps/briefs/brief26.htm