tl;dr: Most likely, the white uniform is meant to reflect a prisoner that has just gone through intake, while the orange jumpsuits represent high-security prisoners. This is a not-uncommon practice in US prison systems.
In real US prisons, uniform policy is entirely up to the local or state prison system, but the system presented in Daredevil does have real-world equivalents. It's very similar to the California prison system, with the colors reversed: an orange jumpsuit is given at intake, until the prisoner is classified into a "security" level and given a new color. (Orange is the New Black shows this same system slightly more accurately) So, for example, general population prisoners in California get white or blue clothing, while high-security prisoners may get something more obvious.
Additionally, in many prison systems, different uniform colors may be used for certain categories of prisoner that have different prison access. For example, again in California, prisoners that are allowed to work on or outside the perimeter have green uniforms.
I'm not sure what New York City (where Daredevil is set) prisoners are wearing these days, but I don't think they actually wear orange jumpsuits. Ironically, the success of Orange is the New Black has made the orange jumpsuit "cool", and is causing problems for a lot of prison systems. Many of them are converting back to the old striped uniforms of the late 1800s.