In streamlines, the test charge used has no mass, or velocity. This means it follows the path of the electric field. Effectively what you should end up with is a limited version of the E-field. To calculate the resultant curves, Coulombs law is used. Streamlines can be drawn off of a voltage potential, or from a point in space. When drawn from a voltage potential, the streamlines will be placed leaving from both sides. From a point in space, the streamline will travel in the direction of increasing or decreasing field.
For the trajectories, a particle is used possessing charge, mass, and velocity. Thus the resultant path does not follow the electric field, but rather a path dictated by F = m a, where the electric field acts on the particle to slowly change its direction. Particles are launched with a user specified velocity, and direction.