What is difference between cost efficiency and cost effectiveness?

Efficiency refers to quantity or speed, effectiveness refers to quality.
Take the example of two Customer Service reps, the first one is very short with the customers. If they start to tell him any unneccessary information, he cuts them off and tells them "that's not important". He quickly resolves their issue but leaves them with a bad taste for the company - most will never be repeat customers. He is able to handle 50 customer calls per day.
The second rep takes time with the customers, shows empathy and concern, reviews the situation with the customer at the end of the call. Every customer is satisfied and impressed - all will certainly do more business with the company and refer their friends. This rep is able to handle 30 customers per day.
The first rep is very efficient, the second rep is more effective.  

Answer

Effectiveness simply relates to reaching goals...so a company that has captured a 75% market share is very effective. Efficiency relates to how much they needed to spend or invest in relation to their effectiveness...so if two companies each had only a 0.1% rejection rate off the assembly line, they would be equally effective - but if the first company invested half as much as the second company in quality control, the first company is twice as efficient as the second company.