In this paper we provide a classification of adaptive systems with respect to the kind of semantic technology they exploit to accomplish or improve specific adaptation and user modeling tasks. This classification is based on a distinction between strong semantic techniques and weak semantic techniques. The former are techniques based on the Semantic Web, while the latter regard technologies that, in different ways, annotate resources, enriching their meaning. This second category includes, in particular, Web 2.0 social annotations and mixed approaches between social annotations and Semantic Web techniques. While the impact of the Semantic Web on adaptive systems has been discussed in several survey papers, the potential of weak semantic technologies has, so far, received little attention. The aim of this analysis is to fill this gap. Therefore, we will discuss contributions and limits of both approaches, but we will focus special attention on weak semantic adaptive systems.