The accounts record of King James IV of Scotland show an invoice for the purchase of golf clubs and balls to the value of 14 shillings dated 21st September in 1502. From the types of the clubs that were purchased he played the long and not only the short game.
This leads me to think that it is logical that the game was first played from short distances into the hole. Therefore presume that as the players got more efficient in holing out the distances were increased up to the point when another club, one with a longer shaft to produce more potential using the same movement, was needed to play the ball to the hole.
The same thought process leads on to think that the percentage of playing the ball into the hole would be more difficult, many times the ball would be a short distance from the hole and to play the shorter distance to complete the play on the hole the short club was used. This club is called the putter.
I believe that the putting stroke is a short version of the full swing!
The backward movement of the putting stroke using only your shoulders is the starting movement for every swing.
So here is a video to help practise and understand putting and the putting stroke (swing).