What you're asking is quite a nuanced question - I'm sure Chris Parker will provide a detailed response that will clarify mine further. 'Jujutsu' schools evolved from earlier systems of battlefield grappling; typically not named jujutsu - yawara, kumiuchi, koshi no mawari, torite and other terms were typically used in these older schools to describe their grappling, which usually involved jujutsu type techniques accounting for the wearing of armour and the use of weapons. In that sense yes, jujutsu styles are 'samurai' in origin, however 'samurai' shouldn't be thought of as an homogenous group, aside from 'the rest'. There were samurai who were farmers, bureacrats, 'police'.. and everything in between. Some early 'jujutsu' type systems which still survive are known as 'farmer' systems.
As I just mentioned.. several koryu jujutsu schools survive today - perhaps visit Martial Arts of Japan: Koryu.com for some background. Some of the older systems are Takenouchi ryu (generally considered the oldest still surviving), Shosho ryu, Araki ryu, Yagyu Shingan ryu and a few others:
Yagyu Shingan ryu
As you can see there is an emphasis on weapons, and deeper stances, due to the use of armour. Later jujutsu systems evolved through the 'peaceful' Edo period to reflect a more unarmoured self defense focus, still often incorporating the use of weapons, but moving away from the battlefield focus of the earlier systems toward smaller, concealed weapons; kodachi, tessen and others are often trained more in the later schools. Examples of these types of systems which survive are Tenjin Shinyo ryu, Shindo Yoshin ryu and Daito ryu.