Neural signals amplitude
Those voltages refer to the difference between the inside and outside of the cell (i.e., -70mV means the cell is 70mV more negative than the outside).

You can't possibly measure that potential difference from outside of a cell. When you do extracellular recording, you are measuring spatial differences in ion concentrations that occur due to ions flowing in and out of cells. For example, when a cell fires an action potential, lots of positive ions flow into the cell; this makes the area just around the cell slightly more negative than an area further away. The magnitude of this potential as measured depends greatly on your recording configuration, the type of signal you are recording (i.e., population activity or just a single cell; synaptic currents versus action potentials), how close your electrode is to the signal you are recording, and where your ground is (or position of both of your electrodes if you are doing a bipolar recording).

Although it varies, in most cases the signals you record extracellularly are on the order of microvolts to a couple of millivolts.