I do not know of any standard name for the upper waveform. Your description seems good! The bottom waveform looks closer to a triangle wave than the shark fin you mention because the capacitor is partially charged when the voltage starts going up or down. The waveform is only part of a full exponential function. It just appears more linear than a larger segment of the function. In other words, the capacitor is not starting at 0 volts or fully charged but somewhere near the middle. The waveform you see can probably be fit to a portion of the classic RC exponential function. Even though it is only a portion, the waveform is still described as "exponential". A classic use of only a portion of the function is a 555 timer.