libcurl keeps a pool of old connections alive. When one transfer has completed it will keep N connections alive in a "connection pool" so that a subsequent transfer that happens to be able to reuse one of the existing connections can use it instead of creating a new one. Reusing a connection instead of creating a new one offers significant benefits in speed and required resources.
When you are using the easy API, or, more specifically, curl_easy_perform(), libcurl will keep the pool associated with the specific easy handle. Then reusing the same easy handle will ensure it can reuse its connection.
When you are using the multi API, the connection pool is instead kept associated with the multi handle. This allows you to cleanup and re-create easy handles freely without risking losing the connection pool, and it allows the connection used by one easy handle to get reused by a separate one in a later transfer. Just reuse the multi handle!