Trashed conversations are not included in searches.
You should archive conversations that have some information value for you in the future. Your searches include archived messages.

Hi Kateryna! Isaiah here from the Support team 

Great question! 

Trashing and archiving a conversation in Front serve different purposes and have distinct impacts:

1. **Archiving a Conversation**:
   - Archiving is recommended for removing conversations from your inbox without deleting them. Archived conversations are still accessible in the Archived tab and can be included in analytics metrics.
   - Archived conversations appear alongside open conversations when searching in Front, making them easy to find later.
   - Archiving is suitable for informational messages or those that don't require immediate action.

2. **Trashing a Conversation**:
   - Trashing moves a conversation to the Trash tab, where it can be restored at any time. However, trashed conversations are excluded from analytics metrics.
   - Trashed conversations are not included in default search results unless you use the `is:trashed` filter.
   - Trashing is more suitable for spam or junk messages, and it is possible to permanently delete trashed conversations if needed.

Overall, archiving is a way to keep your inbox tidy while retaining access to conversations, whereas trashing is used for removing unwanted messages with the option to permanently delete them.