In cricket commentary, some bowlers are called 'chinaman bowlers' and some 'orthodox bowlers'. What type of bowlers are these?
I'm going to add another answer here because I feel the first answer 1/ doesn't fully answer the question and 2/ is a little confusing in its use of terminology and explanation.
What is a Chinaman bowler?
A bowler who bowls chinamans is a left(1) handed spin bowler whose stock(2) ball spins from off stump to leg stump when bowled to a right handed batsman. Sometimes referred to as a left handed off spinner as opposed to a right handed off spinner. The term chinaman differentiates between a left handed off spinner and a right handed off spinner.
A right handed off spinner bowls exactly the same ball as a chinaman (i.e. spinning from off stump to leg stump) with the single difference that it's bowled with the right hand rather than the left.
Also, please ignore any references to finger spin and wrist spin. These are terms to describe how revolutions are imparted to make the ball spin. A finger spinner uses his fingers to spin the ball and a wrist spinner uses his wrist to spin the ball. These have nothing to do with with the direction the ball will spin in or whether it's a left handed or right handed bowler.
Where does the term chinaman originate from?
It comes from the first bowler to bowl in this way - Ellis Edgar Achong
Who was of Chinese decent, hence the term. Read more about him here -
What is a left arm orthodox spin bowler?
This is the term given to left arm(1) spin bowlers who spin the ball in the direction assumed to be natural for a left armed spin bowler whose stock(2) ball would spin from leg stump to off stump when bowled to a right handed batsman.
Hence the term orthodox. We naturally assume when a left arm spinner is mentioned that he will spin the ball in this way.
What is the difference between left arm orthodox and right arm orthodox?
A right handed off spinner is considered to be an orthodox right arm spin bowler as he naturally spins the ball from off stump to leg stump when bowling to a right handed batsman. You'll note this is the same direction as the chinaman. A left arm orthodox spin bowler will bowl the ball in the opposite direction.
What is the right handed version of the chinaman?
That would be the leg spinner, because he bowls the ball to spin in the opposite direction to the orthodox right handed off spinner, i.e. from leg stump to off stump when bowled to a right handed batsman.
You'll notice that the terms used here describe one of two things -
1/ The arm used to bowl the ball, and
Left arm orthodox spins the ball in the same direction as a right arm leg spinner. Right arm orthodox spins the ball in the same direction as the left arm chinaman.
I hope this has helped to clarify this answer.
There are two types of left arm spin bowlers, Chinaman and Orthodox.
Chinaman Bowler or Unorthodox Left arm Spinner- A Chinaman bowler is a left arm unorthodox spin bowler who spins the ball using Wrist spin so that the ball goes from off side to leg side for a right handed batsman. They often use leg break or leg spin for mixing variety.
Example: Michael Bevan(Australia), Brad Hogg(Australia), Sir Garry Sobers and Dave Mohammad(West Indies) etc.
Orthodox Bowler or Orthodox Left arm Spinner- An orthodox bowler is also a left hand bowler but he uses his fingers to spin the ball such a way that it goes from right side to left side of the pitch(from POV of the bowler).
Example: Daniel Vettori(New Zealand), Yuvraj Singh and Pragyan Ojha(India) etc.