This paper presents some relationships among different types of controllability for finite and infinite dimension linear systems. Several authors derived similar results but the framework developed here is claimed to be more general so that other results could be seen as corollaries of the results reported. The tools used to obtain the results are theorems of functional analysis, in particular the Baire category theorem. Using these theorems, relationships among local controllability at time \(t\), and local controllability in free time are derived and characterizations of the corresponding controllable sets are obtained. This paper is of interests mainly to mathematicians.