The anology applies to the ICC, and the FCC (Federal Communication Commission) as well. However, the analogies are specious. Justifications for both ICC and FCC rest on the common carrier doctrine, the upshot of which is that since the government has an integral role in an industry (land grants and subsidies for the railroads―except for a few exceptions, one of which readers of The Golden Pinnacle are aware of―and allocating scarce radio and television spectrum in the case of the FCC) the government is required to regulate that industry. The parental version of the common carrier doctrine: As long as you live in my house and I pay the bills, you play by my rules.
The internet is a privately developed and operated innovation, and the government has never played much of a role, except as a user and now, with the Snowden revelations, as a monitor. By its own terms, the common carrier doctrine does not apply, and so there is no basis for the government's instrusive net neutrality rule. The validity of the common carrier doctrine I'll leave for another day, but in preview, I don't think much of it, either.