  The repeating fast radio burst (FRB) source FRB 20200120E is exceptional
because of its proximity and association with a globular cluster. Here we
report $60$ bursts detected with the Effelsberg telescope at 1.4 GHz. We
observe large variations in the burst rate, and report the first FRB 20200120E
`burst storm', where the source suddenly became active and 53 bursts (fluence
$\geq 0.04$ Jy ms) occurred within only 40 minutes. We find no strict
periodicity in the burst arrival times, nor any evidence for periodicity in the
source's activity between observations. The burst storm shows a steep energy
distribution (power-law index $\alpha = 2.39\pm0.12$) and a bi-modal wait-time
distribution, with log-normal means of 0.94$^{+0.07}_{-0.06}$ s and
23.61$^{+3.06}_{-2.71}$ s. We attribute these wait-time distribution peaks to a
characteristic event timescale and pseudo-Poisson burst rate, respectively. The
secondary wait-time peak at $\sim1$ s is $\sim50\times$ longer than the
$\sim24$ ms timescale seen for both FRB 20121102A and FRB 20201124A --
potentially indicating a larger emission region, or slower burst propagation.
FRB 20200120E shows order-of-magnitude lower burst durations and luminosities
compared with FRB 20121102A and FRB 20201124A. Lastly, in contrast to FRB
20121102A, which has observed dispersion measure (DM) variations of $\Delta{\rm
DM} >1$ pc cm$^{-3}$ on month-to-year timescales, we determine that FRB
20200120E's DM has remained stable ($\Delta{\rm DM} <0.15$ pc cm$^{-3}$) over
$>10$ months. Overall, the observational characteristics of FRB 20200120E
deviate quantitatively from other active repeaters, but it is unclear whether
it is qualitatively a different type of source.
