Rupa Goswami defines japa in the Bhakti rasāmṛta sindhu (1.2.149-151) as follows:
mantrasya sulaghūccāro japa ity abhidhīyate ||
Here, sulaghūccāraḥ = su + laghu + uccāraḥ. uccāraḥ means pronunciation. Laghu means light. Su-laghu is very very light, i.e. inaudible.
The translation then is
Inaudible chanting of the mantra is called japa.
The Hari bhakti vilāsa mentions three types of japa: mānasika (in the mind), upāṁśu (chanting very softly), and vācika (audible). It is therefore interesting that Rupa Goswami’s Bhakti rasāmṛta sindhu, which is specifically written for Caitanya Vaisnavas, instructs that chanting be done inaudibly, which means upāṁśu japa.
As discussed elsewhere, bhakti is ultimately a matter of the mind. Therefore, whichever japa one does, the focus of the mind on the japa is all important. As a result, mānasika japa is the most effective types of japa.
Rupa Goswami defines kīrtanam (1.2.145-146) as follows:
nāma-līlā-guṇadīnām uccair-bhāṣā tu kīrtanam – the loud singing of the name, līlā and qualities of Kṛṣṇa is called kīrtana.
Rupa Goswami also distinguishes kīrtana, singing in a group, from gītam which is sung by oneself.