Hi Brandon,
I agree, it sounds like it's probably a traditional Japanese jujutsu style. Assuming it is, and having made a very similar transition myself many years ago (from jidokwan to jungki hapkido ,which is almost pure jujutsu - none of the fancy kicks/meditation/philosophy that Ji Han Jae added to hapkido. Also did Daito-ryu aikijujutsu for a couple of years), I think I can give you a couple of pointers.
First, forget every formal stance you ever learned. Traditional jujutsu is all about quick, effective movement and keeping yourself balanced always. You'll find that something like a boxer's stance is very common. In a boxer's stance, you're light on your feet and mobile in pretty much any direction.
Second, no forms. You will find a new form of "kata."
Kata in Japanese jujutsu is the classic way of transmitting the art: two-man practice, uke and tori, of individual techniques, with predefined attacks and predefined defenses.
Third, a different approach to striking. One of the things that always surprised me about the original form of hapkido, from Choi Yong Sul, is that there is no strike that resembles the classic karate fist punch or Western boxing punch. There are many different hand and elbow strikes, and even inner-wrist strikes, but they're a bit unusual and mostly aim to affect a nerve or other vital point to set up a lock or throw. No "one strike, one kill" idea here.

One more for now... you'll have to get used to getting your wrists, elbows and shoulders locked and cranked. At first - as in for the first six months or so - it can be very uncomfortable. But you will start to get used to it over time, and with the joint limbering and stretching that is part of any good jujutsu/hapkido program.
As for gi/no-gi - that's a BJJ/MMA consideration only - irrelevant to Japanese jujutsu. You will definitely wear a gi, most likely a judogi. Judo gis are good for jujutsu because you use the gi a lot in both offense and defense, and it is subject to quite a bit of stress. A typical karate gi won't stand up long to the rigors of jujutsu. Some styles also use the hakama (Daito-ryu practioners in Japan almost always use the hakama; in the US, it tends to be only for the yudansha).
Can't think of any other obvious differences at the moment, but I'll come back when I can. And good luck to you.
Take care, Howard