A ceremony dating from Vedic times in which oblations are offered into a fire built according to scriptural injunctions; a ritual to communicate with God, Gods and devas. Also called yajna or havan.
Homa,Homam,yajna or havan, is fire worship.Homa is done to enhance the effects of Japas.When the japa is done without any desire, it needs no fire worship.

In short the difference between a simple Puja and homa is that In Puja, mantras are recited and flowers are offered by the temple priest whereas in Homas, fire, oblations and mantras are used.