To be simple one can say:
Variation: one musical theme/melodic material that already has been presented is the object of the variations. Variations of that material (one already existing material/melody/theme). Variations normally don't change the melody content neither interrupt/cut pieces out of the original material, but can be very creative with all other aspects like rhythm, dynamic, note length and ornaments.
Development: works the material already presented also, but here the melodic material can be developed/altered and/or presented just fragments of the original material; it is also possible the development will include material from other melodies/themes that have already been presented.
It is posible that a variation is very complex, with tonality changes, ornamentations or other changes to the melodie aspect, so it looks like a development, but still only one melody/element at a time.
It is also possible a development to keep the ideas of the theme melody, so it can look like a variation. Still the idea of variations is to use one theme/melody presented and keep the melodic material quite "original", the development going "forward" in music making a sum/resume of one or many ideas presented and/or even with new melodic/harmonic changed to that material.
There is a line of composition called "Developing variation" which makes variations using serial and mathematic models to make variations of a theme, this produces music that is sometimes difficult to associate with the theme and thus is a "developing variation".
Found this related in wikipedia: