Welcome, bercam.
Present participles (e.g.,
meeting) express that an action is taking place - that it's been actualized, whereas infinitives (e.g., to meet) express that an action hasn't happened yet - it's unactualized. That's why "to meet" is used as a greeting and "meeting" as a farewell,
[1] Nice to meet you. <introduction>
[2] Nice meeting you. <closing>
Hope that helps.
