The Spanish word 'hospedaje' (meaning 'lodging' or 'accommodation') comes from the Spanish verb 'hospedar' ('to lodge' or 'to host') combined with the noun-forming suffix '-aje'. The verb 'hospedar' itself derives from the Latin verb 'hospitari', which meant 'to give lodging'. The suffix '-aje' was added to transform the verb into a noun that refers to the act or service of providing lodging.

Several common Spanish words share this same Latin root, including: 'huésped' (guest), 'hospital' (hospital), 'hostal' (hostel), and 'hospicio' (hospice). All these words relate to the concept of hosting or providing shelter to others.

English speakers might recognize the connection to several familiar words that come from the same Latin root, such as 'hospital', 'hostel', 'hospice', 'host', 'hotel', and 'hospitality'. All these words share the core meaning of providing shelter or care to others. The English word 'host' can be both a noun (someone who receives guests) and a verb (to receive guests), similar to how the Spanish 'hospedar' relates to 'hospedaje'.