Historical heritage is all the objects and buildings remaining from the past which are valued for the knowledge they provide about societies living before us.
Archeological heritage and architectural heritage are two components of historical heritage.
Archeological heritage is all the objects that can be studied using archeological methods such as bones, old coins, pottery, tools etc. An important archeological site in Tanzania is Olduvai Gorge (http://en.wikipedia.org/wiki/Olduvai_Gorge) where the remains of humans who lived on the site some two million years ago have been excavated and are being studied.
A list of other archeological sites in Tanzania can be found here http://en.wikipedia.org/wiki/Category:Archaeological_sites_in_Tanzania
Architectural heritage is all buildings and structures that have value because of their historical, archaeological, artistic, scientific, social or technical interests. For example Swahili architecture along the Tanzanian coast tells us something about the Arabic or Islamic influences on local customs.
Culture is the behaviors of people in an area and the way they relate to each other. Culture is also a reflection of the way a group of people see and represent the world. Culture has a material component, made up of physical artifacts made by a group of people. 
So cultural heritage is what remains of physical objects and other qualities that tell us about a certain group or society. Examples are manners of dress, song and dance inherited from past generations, and maintained in the present, likely to be passed on to future generations. In Tanzania, some Maasai wear distinctive traditional clothing and jewelry, and maintain traditional roles in their society determined by their age group: http://en.wikipedia.org/wiki/Maasai_people.
Over 120 groups with a unique cultural heritage exist in Tanzania. See the list here: http://en.wikipedia.org/wiki/List_of_ethnic_groups_in_Tanzania
See the standards and toolkit for the cultural heritage toolkit click here>