The way Europeans viewed property ownership in the New World was by and large influenced by the "discovery doctrine," wherein any land in the New World belonged to whichever European power discovered it first (assuming the colonial territory hadn't been seized by another European power). When it came to individual land ownership, Europeans believed that all land had a rightful owner, and that land could be passed from one individual to another via inheritance or purchase.
The way natives viewed property ownership is a little bit more complicated simply due to the fact that "Native Americans" were not (and are not) a single cohesive group with the same belief and traditions. Some Native groups, like the Iroquois and the Wendat (aka the Huron) believed in communal land ownership, wherein a permanently settled plot of land belonged to all the people of the tribe, and would only change hands if conquered by a different tribe. Nomadic native groups, like the Sioux, didn't believe in land ownership at all, and thus had no real concept of it. Finally, some native groups such as the Aztec and Incan empires believed in roughly the same ideas of property ownership as the Europeans (land has rightful individual owners, and can be purchased by individuals and inherited).
The Europeans have a perspective of owning land is considered when someone plants or builds a structure in it. On the other hand, Native Americans think that simply living on the land is already enough for them to be considered as their own property.
Elected officials who are sent to a government seat to do the will of the people from their designated districts are called "representatives", since the "represent" the people who elected them.
