Room Separator

A threshold.

a saddle is used to bridge a bathroom and bedroom.

A transition piece.

Rogman-
Thank you. I believe you are correct though I can not find it in the dictionary.

i believe chai2 is also correct...
http://www.hgtv.com/home-improvement/floor-threshold/index.html

It is my understanding that if you have a tiled area say in a bathroom or hallway to a kitchen, the separator is called a saddle (marble or other like material). If it's for a room area that might be going from a wood floor to another wood floor, it can be called a threshold.

Perhaps it is regional? the only term I've ever heard/seen for that piece is threshold.

http://www.schluter.co.uk/floor_trim_profiles.aspx

http://www.johnbridge.com/vbulletin/archive/index.php/t-37285.html

http://www.ehow.com/how_4486714_install-threshold-over-wood-flooring.html

http://www.diynetwork.com/floors/carpet-thresholds/index.html