QUICK ANSWER
"Veloz" is an adjective which is often translated as "fast", and "rápido" is an adjective which is also often translated as "fast". Learn more about the difference between "veloz" and "rápido" below.
veloz(
beh
-
lohs
)An adjective is a word that describes a noun (e.g., the big dog).
1. (general)
a. fast
Nos montamos en uno de los trenes más veloces del mundo en Japón. We rode one of the fastest trains in the world in Japan.
c. rapid
El crecimiento veloz de la economía se debe a iniciativas financieras nuevas.The rapid growth of the economy is due to new financial initiatives.
e. expeditious (formal)
La ruta 5 permite un tránsito veloz entre Los Ángeles y San Francisco. Route 5 allows for an expeditious trip between Los Angeles and San Francisco.
rápido(
rrah
-
pee
-
doh
)An adjective is a word that describes a noun (e.g., the big dog).
An adverb is a word that describes a verb, an adjective, or other adverbs (e.g., to run quickly, very tired).
A masculine noun is used with masculine articles and adjectives (e.g., el hombre guapo, el sol amarillo).
3. (rail)
a. express train
Cuando fuimos a Japón, tomamos el rápido a Tokio.When we went to Japan, we took the express train to Tokyo.
b. fast train
Los planes para tener un rápido entre Los Ángeles y San Francisco han quedado truncos.Plans for a fast train between Los Angeles and San Francisco are incomplete.