Right Handed spin bowlers

Off spin / Off break:
A slow ball which turns towards the bowling hand side of the bowler after pitched. The spin is produced mostly by Fingers

For a right handed bowler, the ball will turn towards the right side of the bowler and a RHB will see the turn as Off to Leg direction.

For a left handed bowler, the ball will turn towards the left side of the bowler and a RHB will see the turn as Leg to Off direction. (See SLA below)

Leg spin / Leg break:
A slow ball which turns opposite the bowling hand side of the bowler after pitched. The spin is produced mostly by Wrist.

For a right handed bowler, the ball will turn towards the left side of the bowler and a RHB will see the turn as Leg to Off direction.

For a left handed bowler, the ball will turn towards the right side of the bowler and a RHB will see the turn as Off to Leg direction. (See SLC below)

Left Handed spin bowlers

Left-arm orthodox spin:
Left-handed Off spin. Generally called Slow Left Arm (SLA).

Since this is Off spin, the ball will turn towards the left side (bowling hand side) of the bowler and a RHB will see the turn as Leg to Off direction (just like leg spin).

Left-arm unorthodox spin:
Left-handed Leg spin. Generally called Slow Left arm Chinaman (SLC).

Since this is Leg spin, the ball will turn towards the right side (opposite the bowling hand side) of the bowler and a RHB will see the turn as Off to Leg direction (just like off spin).

Variations: These are surprise deliveries to fool the batsman.

Googly and Chinaman:
Off spin bowled with a Leg spin action and grip by a right handed bowler is called Googly.
Off spin bowled with a Leg spin action and grip by a left handed bowler is called Chinaman.

Googly bowlers are basically Right handed Leg spin bowlers and
Chinaman bowlers are basically Left handed Leg spin bowlers (Left-arm unorthodox).
Both Googly and Chinaman are called Wrong-un in Australia (and now by many as well).

Off spin bowlers produce off spin with off spin action and grip, not with leg spin action and grip. That’s why they are not called Googly or Chinaman bowlers.

A RHB will see Googly as Off spin (Off to Leg) and Chinaman as Leg spin (Leg to Off).

Arm Ball:
Spin bowler sometimes make a delivery with more pace but without spin to fool the batsman.

Doosra:
Leg spin bowled with an Off spin action and grip. Doosra bowlers are basically Off spin bowlers. No separate name for right or left handed bowlers, yet!

Leg spin bowlers produce leg spin with leg spin action and grip, not with off spin action and grip. That’s why they are not called Doosra bowlers.

Top Spin / Over spin:
Forward spin. Ball "shoots" speedier after pitched.

Flipper / Under spin:
Back spin. Ball "flipps" slower after pitched. Extra flight sometimes causes the ball to be dropped closer to the batsman than anticipated.