> There is no difference hardware-wise
The difference between sophisticated (Google, Amazon, Facebook) cloud data centers and traditional corporate data centers is Extremely Large™. Traditional ones are characterized by things like big central UPS systems, redundant AC/DC power supplies in each host, remote-control PDUs, overblown air conditioners, etc. Cloud data centers are typified by non-redundant power supplies with either distributed UPS systems, or no UPS, DC-to-point-of-load, and marginal ventilation where the cold aisles are hotter than the hot aisles of traditional data centers.
> Internet infrastructure as a whole was estimated to use several percent of the world's electricity
Well, if you define "several" as "almost 2%" then yes, but mostly in traditional data centers. Moving to clouds improves this figure. It is estimated that half of global IT power consumption is in cooling and power delivery, meaning the industry as a whole has a PUE of 2.0, whereas Google, Facebook, and Amazon have PUEs of about 1.1. In other words, moving workloads to the cloud can save almost half of the power.