What exactly is the signal strength seen in API for BT/WiFi receivers?
The dBm level specified by a receiver is normally the minimum antenna power it needs to successfully (within a certain prescribed bit error rate) demodulate the data and function as one half of the data link.

It is an absolute measurment of power. Say a reciever requires -100 dBm to function properly; the 100 dB part means 0.1 nano-something and the "something" (the m bit) is specifically milliwatts. So -100dBm = 0.1 nano milliwatts or 0.1 pico watts.


  Is this the difference between the noise and signal


Noise is accounted for if the dBm number applies to a reciever. There is a general formula that assumes a small bit error rate (errors are produced by noise) and local antenna temperature (temperature creates noise).

The transmitter might emit 100 mW but it emits it in a lot of directions just like a lightbulb emits light in a lot of directions simultaneously. So in one specific direction the power, along the line of the target receiver is a massive fraction of what the transmitter is emitting at its antenna.