The distinction is getting slimmer and slimmer, only reason we have the distinction is because MMA is so new as a sport that most fighters coming into the sport come from a different fighting style background from before the time MMA even existed or at least evolved into its own discipline.
The truth is if you are to divide the 2 styles you have to watch them in there pure competitive format because once they are combined within an MMA octagon it becomes MMA grappling, hell even the wrestling style take downs are becoming more and more combined into the striking as the sport evolved and the end result is a completely different from or stand up from any other combat sport due to the need to both be set ready to defend or attack with the take down, so in effect what you are seeing is not boxing or kick boxing or muay thai, what you are seeing is fighters coming from these backgrounds and developing new and often unique forms of MMA style stand up, which is very broad depending on many factors from the size and physical aspects of the individual to past training or even in many cases the different camps where they train, different training partners and coaches, and most importantly what the individual is most at comfort with.
In a sense as the sport evolves we a seeing many individuals pick up unique styles as a result of the endless combos of different factors effecting the development of each individual, in a sense Martial Arts its self is evolving and its doing so around individual needs, skill sets and comfort zones, as oppose to the development of a set style that is supposed to work for everyone, hope that makes sense.
For a start a lot of Jujutsu is lost when you loose the Gi so what you are seeing is more resemblant of a submission style of wrestling with every non-Gi Sumbission from the Jujitsu library there at the disposal as well.
I suppose the main difference is Jujitsu more about transition from one position to another and counter transitions of positions where the end goal is to out remover your opponent on the ground until you have a solid position to lock in a match winning submission.
Where as wrestling is more about dominant power and imposing dominant position and keeping it locked down, except fighters in MMA break in and out of the lock down holds to create space and cause damage (i.e. GnP) which is mostly done in short blasts but again differs from the pure form of wrestling and becomes a new developed MMA skill set.
But the use of both intertwined is more what MMA is all about now, so singling out one from the other is becoming harder to define and pointless, since every fighter comes in with a almost unique skill set despite there base training which would have certainly been developed anyway to better suit the rules of the Octagon, so to some extent there is no exclusive styles that one fighter uses, they will without doubt train all popular styles and combine even if there unique styles does resemble one style stronger than another does not matter because its not pure wrestling or Jitsu that is ever used in the Octagon any more its always mix these days and to different levels of influence from one style to another.