Nanocellulose (NC) suspensions can form rigid volume-spanning arrested states (VASs) at very low volume fractions. The transition from a free-flowing dispersion to a VAS can be the result of either an increase in particle concentration or a reduction in interparticle repulsion. In this work, the concentration-induced transition has been studied with a special focus on the influence of the particle aspect ratio and surface charge density, and an attempt is made to classify these VASs. The results show that for these types of systems two general states can be identified: glasses and gels. These NC suspensions had threshold concentrations inversely proportional to the particle aspect ratio. This dependence indicates that the main reason for the transition is a mobility constraint that, together with the reversibility of the transition, classifies the VASs as colloidal glasses. If the interparticle repulsion is reduced, then the glasses can transform into gels. Thus, depending on the preparation route, either soft and reversible glasses or stiff and irreversible gels can be formed.