Below is the large signal circuit diagram for common emitter, base, and collector configuration just for clarity of visualization.
The voltage source is where the input voltage is applied and the arrow pointer indicates on what port and in what direction the input current is measured.
But, there is a catch, the plotted graphs use different reference terminal. The horizontal axis of your first graph referenced the input voltage at the base to the emitter, therefore, higher base to emitter voltage does indeed increase the base current because the Base-Emitter junction will be more forward-biased, therefore there is an increase in the diffusion emitter current, and therefore there is also an increase in the recombination base current. It is basically a diode equation curve.
Now, for your second graph, the horizontal axis is instead the collector voltage referred to the base. Because we know the collector is at a fixed supply voltage (look at the diagram), increasing the collector to base voltage is, in reality, decreasing the base voltage referred to ground. Based on the same reasoning as before, decreasing the base voltage results in a decrease in base current. So the curve is basically the first curve, but flipped horizontally and then offset to the right by VCE (which is equal to the supply voltage). Remember, VCB = -VBE + VCE.
How about the common base? The graph you have seen will most likely be a graph with a horizontal axis of base voltage referred to the emitter voltage. Therefore, an increase to the base-emitter voltage, again, results in an increase in the emitter current (look at the graph, the input current is now the emitter current). So it will look basically the same as the first graph, but scaled by a factor of 1/(1-alpha).