OK, rise time is usuaslly defined from 10% to 90% of the steady state excursion.
When there is an RC circuit, the waveform is exponential.
When a cap is charged with a constant current source the result is a linear ramp.
The "straight line" you are seeing may just be an artifact of the scope set at Auto trigger or the sweep speed isn't slow enough, so it isn't a line.
Rise-time/Fall time and reset pulse are probably all appropriate.
When there is an RC circuit, the waveform is exponential.
When a cap is charged with a constant current source the result is a linear ramp.
The "straight line" you are seeing may just be an artifact of the scope set at Auto trigger or the sweep speed isn't slow enough, so it isn't a line.
Rise-time/Fall time and reset pulse are probably all appropriate.