Controllers are input widgets that allow you to use a control signal like Velocity, Keytrack or unison as a source signal for a module input. You could already do this but they have been improved both graphically and feature wise. Most controllers now have a popup panel with extra settings so you can customize how they work. For Velocity you can select response curve, for Ketrack you can change mapping, for Unison you can select a specific value for each voice.
Modifiers are like controllers except that they modify an existing input. So you can set Velocity to control the input level of an ADSFR signal. Or you can use the ModWheel modifier to change how much LFO is applied to the pitch input.