Snapchat does not provide a specific feature to determine if someone added you through a quick add or via search. The app doesn't give users detailed information about how they were added to another person's friend list.
Here are some general points to keep in mind:
Quick Add: When someone adds you through Quick Add, it means that Snapchat suggested your profile to them based on mutual friends or similar contacts. They may have seen your username in the Quick Add section and decided to add you.
Add via Search: If someone added you by searching for your username, they likely entered your specific username in the search bar and found your profile that way.
Snapchat generally keeps the process of adding friends private to respect user privacy. The app doesn't provide notifications or indicators to inform you how someone added you as a friend. Snapchat's focus is on connecting users with their friends and people they might know, while also respecting the privacy of its users.
Keep in mind that app features and privacy settings may change over time, so it's always a good idea to check Snapchat's official support or help center for the most up-to-date information on app functionality and privacy.