Executive Search means that you’re looking to recruit someone to your team within (usually) a short time frame to fulfil a specific need or requirement, and in order to fill a vacancy.
Talent Acquisition, on the other hand, is the process of strategically looking for specialists, leaders, future executives, or other qualified professionals for a specific position you anticipate wishing to fill in the future, be it as part of your broader Succession Planning or to lead a specific product such as a new product launch.