You have to be in Setup to search for objects in both Lightning and Classic.
In Classic, you'll find standard objects under Customize in your Setup navigation menu, or you can type their name in the Setup quick find box to narrow down the menu. You'll find custom objects under Build: Create->Objects. The Classic Setup quick find box does not find custom objects by their names unless you hit Enter to perform an advanced search.
Custom objects in Classic setup:
Standard objects in Classic setup:
In Lightning Experience, you'll find both custom and standard objects in Object Manager in Setup, and both custom and standard object names can be searched in the Setup Search box as well as the Quick Find box in the Object Manager tab.
Filtering in Lightning Setup Object Manager:
Filtering in Lightning Setup: