You may type them in your browser, choose images and you will see the difference.

Natasha has suggested a very helpful method. It's a pity it works mainly with nouns :(

Коробка is made from cardboard, ящик is made from wood (sometimes from metal, as postbox, or from plastic, as toolboxes). In addition, drawer is translated as ящик too.

Adam, ящик: (1) drawеr (2) box, hard, oftеn crudе. In this mеaning it ovеrlaps with 'коробка', so you chosе thе word assording to... wеll, collocations, look, matеrial, еtc. Thеrе arе sеvеral factors, thе rеsult is ambiguous somеtimеs. Also, thеy arе synonyms. I can call most of коробка's "ящик", and I can call most of ящик's "коробка" just by mood. And I do that somеtimеs.

Коробка - упаковочный материал, тара, как правило одноразовый. Ящик - как правило не одноразовый, в столе выдвижные ящики, в шкафу, почтовый ящик и т.д.