Under current FCC regulations, it is illegal to "degrade" internet data transfer based on "content, application, or service", so for example if I am connecting to Netflix, my ISP cannot "disprefer" my packets (that would slow down data transfer).
Since "net neutrality" is a meme and not a well-defined legal thing, it's hard to tell. In particular, to know what the result of an upcoming rule change will be, we will have to know what the proposed rule is. If the rule revokes [47 CFR 8.7], there are a number of possible changes in how things work. One would be that maybe Comcast will decide that it will no longer forward packets to or from Time Warner, which would completely cut the cord between those ISPs. For obvious business reasons, this will not happen. But in terms of a legal "could it happen?", that and a lot of other things could theoretically happen. It just depends on what the final rule is.