The main difference is in the internal temp rating the item has.
" Note 2: The LTM4628 is tested under pulsed load conditions such that TJ ≈ TA. The LTM4628E is guaranteed to meet specifications from 0°C to 125°C internal temperature. Specifications over the –40°C to 125°C internal operating temperature range are assured by design, characterization and correlation with statistical process controls. The LTM4628I is guaranteed over the full –40°C to 125°C internal operating temperature range. Note that the maximum ambient temperature consistent with these specifications is determined by specific operating conditions in conjunction with board layout, the rated package thermal impedance and other environmental factors. "