The 助 in 助手 means a person who helps.
The 助 in 救助 expresses helping or rescuing.
assistant; helper · research assistant; teaching assistant
rescue; relief; aid
advice; counsel; suggestion
assistance; support; subsidy
promotion; encouragement; fostering · unwanted help; unnecessary help; disservice
assistance; support; help
midwifery
help; assistance; aid
particle; postpositional particle
aid; help; assistance; support
assistance; support; backing · aiding and abetting; abetment
assistant professor; associate professor
supporting performance; playing a supporting role
approach run; run-up
self-help; self-reliance
mutual aid; cooperation; mutual benefit
assistant official; deputy mayor
assistant director
a small help; some assistance; an aid
sparing a life; clemency · reconsideration of dismissal
inflecting dependent word; bound auxiliary · auxiliary verb (non-Japanese)
support; patronage; backing
midwife
mutual aid; cooperation
wife's help; support from one's wife
divine help; heavenly assistance
binding particle (abbreviation)
public assistance
The kanji 助 is used as a prefix in Sino-Japanese compounds, derived from its meaning 'help' or 'assist'.