Difference between ESOP-8 and SOP-8?
Package naming is not very standardized. Different vendors can use different names for the same package or the same name for different packages. 

It looks like both the parts you have linked are in a variant of SOP-8 with a large pad on the bottom for better thermal dissipation, which is being variously reffered to as "ESOP-8" (tpower LCSC page), "SOP8-PP" (tpower datasheet), "SOP-8_EP_150mil" (nanjing LCSC page) and "8 引脚 SOP-PP" (nanjing datasheet)

(note: I can't actually read any of the text in the data sheets, but it was fairly easy to find the package diagram)