Wireless Access Point Added To A Router?

I currently have the following network configuration:- Broadband Cable Modem (in my den) - Router (in my den) - Computer (in my den) - Wireless Access Point (family room)My broadband cable modem is connected to my router via ethernet cable. I also have an Ethernet cable running from the back of my router directly into my PC. My current setup is in my den (I will explain). In my family room (which is away from the den) I have my television and several other wireless devices (Roku box, etc). My signal strength is low in my family room due to many walls between my den and family room. I therefore installed a Wireless Access Point in my family room by running an Ethernet cable into my basement and connecting the router in the den to the Wireless Access Point in my family room. Now here is my question: I set the SSID (or network name) of the Access Point so that it is the same as my current network name (that way I see the AP on the network). Now here is where I need to understand how a wireless Access Point works. If I have a laptop or other wireless device in my family room and search for a wireless signal, am I connecting to my router (that has a weaker wireless signal than the AP) or to my Access Point (stronger because my Access Point is a foot away from my wireless devices) since they both have the same network name? And if I connect at that strong signal and walk into another room where the signal is weaker, does my laptop automatically connect to the wireless router? How do I tell if both my router an wireless Access Point are using the same SSID or network name. I guess what I'm trying to ask is where am I getting my wireless signal from, the Access Point or the Router or both (assume I am in wireless mode).