Output characteristics of transistor
The difference needs no transistor physics, it's pure current summing case.

Physically transistors work equally in CE and CB configurations. The slope in the upper curve set shows the dynamic conductance increase between C and E when Ib gets bigger; Ic vs Vce climbs steeper with bigger Ib (see NOTE1)

The same physics happen inside the transistor also in CB configuration, current Ie contains all Ic plus the base current which is say one percent of Ic. When the curves are drawn with separate constant Ie values, the growth of Ic due the growth of Vce is excluded from the drawing by the maker of the drawing. 

NOTE1: the increase of Ic when Vce grows is considered harmful in applications where transistor is used as amplifier. It causes loss of gain, because the equivalent dynamic conductance eats a part of the output signal power.  Fortunately transistors have been 50 years so good and available with so low cost that this is not a serious obstacle for good designs.