Search phrase suggestions and product suggestions can always be turned off. How you do this, depends on your platform and type of implementation.

Magento 1
To turn suggestions on or off in Magento 1, go to the CMS: Module 'System' > Configuration > Catalog > Tweakwise.
Open the tab Search Autocomplete.

Choose Enabled > Yes to start using suggestions and choose No to turn off all suggestion types. Use the options Add products and Add suggestions to display product suggestions, search phrase suggestions, or both.  The option Max results is the number of suggestions that need to be available to start showing autocomplete results. And Minimal search characters to start autocomplete search lets you decide after how many character entries you want to start displaying suggestions.

Choose Stay in category > Yes to display autocomplete suggestions within the active category in Magento. If there is no active category (for example when requesting a CMS page or the home page) this option will have no effect on the results.

Magento 2
To turn suggestions on or off in Magento 2, go to the CMS: Module ‘Shops’ > Configuration > Tweakwise.
Open the tab Autocomplete.

Choose Enabled > Yes to start using suggestions and choose No to turn off all suggestion types. Use the options Add products and Add suggestions to display product suggestions, search phrase suggestions, or both.  The option Max results is the number of suggestions that need to be available to start showing autocomplete results. Choose Stay in category > Yes to display autocomplete suggestions within the active category in Magento. If there is no active category (for example when requesting a CMS page or the home page) this option will have no effect on the results.

Other implementations
Please contact the developer of other platforms and implementations to disable suggestions.