In Engpsh, there are several ways to express the idea of existence or occurrence. Here are a few options:

To exist:

To be present or in existence
To have being or reapty
To have a physical presence or material form

To occur:

To happen or take place
To come into being or to be found to exist
To happen as an event or incident

Examples:

The tree exists in the park.
The event occurred last night.

I hope this helps! Let me know if you have any other questions.