What's a searching kiss?

According to japanese sources, it's a kiss where you move your tongue around in your partner's mouth, like along the teeth, rubbing the roof of their mouth, etc. as if it's "searching" for something. Hence the level of difficulty to make it feel nice.

Inb4 the mysterious girl is Kanon from a different future that made a contract with a higher being to be able to help humanity but failed and now she regrets it and tries to change the past

That was my exact thought the instant I saw that they looked so much alike, and her eyes are hidden!