They are both very common verbs with lots of meanings. For example:
KEEP --
to keep something for somebody - guardar algo para alguien
to keep something from somebody - ocultar algo a alguien (information)
to keep one's job - conservar el trabajo
to keep its shape - no deformarse (garment)
to keep its color - no desteñir (garment)
to keep somebody's attention - mantener la atención de alguien
keep the change - quédese con el cambio
to keep a diary - llevar un diario
to keep a note of something - llevar cuenta de algo
to keep order - mantener el orden
to keep a record of something - registrar algo
to keep a secret - guardar un secreto
to keep something clean/secret - mantener algo limpio/en secreto
to keep somebody awake - mantener or tener despierto(a) a alguien
to keep somebody waiting - tener a alguien esperando
HOLD --
to take hold of - agarrarse a
to hold something in position - sujetar algo sin que se mueva
to hold somebody prisoner - retener a alguien como prisionero
the police are holding him for questioning - la policía lo tiene retenido para interrogarlo
to hold somebody's interest/attention - mantener el interés/la atención de alguien
to hold somebody to his promise - hacer que alguien cumpla su promesa
to hold one's breath - contener el aliento