In fluid dynamics, streamlines are considered to be independent of time, while streaklines represent time-dependent vector fields. Imagine a non-stationary flow, i.e. the vector field representing the flow changes at each delta-t. A streamline would be computed/displayed throughout the spatial field, but just at a snapshot in time. A streakline, on the other hand, would begin at some starting position (in space & time) and would vary from a streamline when the next delta-t (and accompanying vector field) was known, then again at the next delta-t, etc.