to affect means that something changed your situation, some external factors made you change.
The crisis affected a lot of people.
to influence means that something changed your emotions or attitude and thus made you change your behaviour.
He is a person that influences people.
That’s why things without emotions are mostly affected.
The teenager's video game playing affected his grades.
Almost 800 hectares of bananas in Ecuador were affected by cold, rains, and ash.
Note:
В значении "влияние НА" существительное "influence" используется с предлогом "ON"
