It has recently been suggested that random telegraph noise (RTN) and the bias temperature instability (BTI) are due to similar defects. Here we thoroughly analyze this hypothesis using nano-scale devices to show that (i) all defects that contribute to BTI recovery can also become spontaneously charged to produce an RTN event, (ii) most RTN defects also contribute to BTI recovery, (iii) the distribution of step-heights, capture and emission times is equally wide and similar for RTN and BTI, and (iv) both RTN and BTI defects are volatile, meaning that they can disappear and reappear. From these observations we conclude that RTN and the recoverable component of BTI are very likely due to the same defects. As a very important consequence, RTN and BTI must be analyzed and guardbanded against together. In particular, since conventional RTN analysis dominantly captures defects with the strongest contribution to the noise power, it misses the defects with large capture times. As we will show, however, it is exactly these defects with large capture times that may by chance become occupied at the same time after long times, thereby leading to very large NBTI-like threshold voltage fluctuations in an RTN setting. Conversely, conventional BTI analysis based on the expectation value of the stochastic trap behavior misses these RTN-like fluctuations when extrapolated down to operating voltages, potentially leading to wrong conclusions.