You seem to be describing a single press gesture.
I would call it a single press. I believe your understanding of touch gestures might be wrong, as I would not call the event you describe a touch gesture. I would call it a response to a particular touch gesture.
Let's break down your description into the action and the reaction.
the user touches a point on screen
That, in itself, completely describes the event where the user interacts with the screen. This describes the interaction where a user simply touches the screen; a single press.
an object moves (ease-out) to the location where the finger is touching the screen
This is your reaction to the gesture of touching the screen. If you wish to describe the event, I would call it a "mouse follow" or "beacon follow", where your element follows the mouse cursor (excuse the analogy) or a beacon that you place down during your input.
Can you tell me the names of the different types of multi-touch gestures (screen-based) such as tap, swipe, etc.?
To me, this appears to be a difficult question, especially given the lack of context. Do you simply wish to know of the alternates available to you through a multi-touch input device, or do you actually wish to know for the purpose of deliberately implementing them? Different platforms can have different names for the same gesture, and as a result, names you hear might be correct but not actually work if taken literally in implementation.
- Long press
- Press and hold
- Pinch in
- Pinch out