The main difference between fast and slow stochastics is summed up in one word: sensitivity. The fast stochastic is more sensitive than the slow stochastic to changes in the price of the underlying security and will likely result in many transaction signals. However, to really understand this difference, you should first understand what the stochastic momentum indicator is all about.
The stochastic momentum oscillator is used to compare where a security's price closed relative to its price range over a given period of time. It is calculated using the following formula:
%K = 100[(C – L14)/(H14 – L14)] 
C = the most recent closing price
L14 = the low of the 14 previous trading sessions
H14 = the highest price traded during the same 14day period.
A %K result of 80 is interpreted to mean that the price of the security closed above 80% of all prior closing prices that have occurred over the past 14 days. The main assumption is that a security's price will trade at the top of the range in a major uptrend. A threeperiod moving average of the %K called %D is usually included to act as a signal line. Transaction signals are usually made when the %K crosses through the %D. Generally, a period of 14 days is used in the above calculation, but this period is often modified by traders to make this indicator more or less sensitive to movements in the price of the underlying asset. The result obtained from applying the formula above is known as the fast stochastic. Some traders find that this indicator is too responsive to price changes, which ultimately leads to being taken out of positions prematurely. To solve this problem, the slow stochastic was invented by applying a threeperiod moving average to the %K of the fast calculation. Taking a threeperiod moving average of the fast stochastic's %K has proved to be an effective way to increase the quality of transaction signals; it also reduces the number of false crossovers. After the first moving average is applied to the fast stochastic's %K, an additional threeperiod moving average is then applied  making what is known as the slow stochastic's %D. Close inspection will reveal that the %K of the slow stochastic is the same as the %D (signal line) on the fast stochastic.
An easy way to remember the difference between the two is to think of the fast stochastic as a sports car and the slow stochastic as a limousine. Like a sports car, the fast stochastic is agile and changes direction very quickly in response to sudden changes. The slow stochastic takes a little more time to change direction. Mathematically, the two oscillators are nearly the same except that the slow stochastic's %K is created by taking a threeperiod average of the fast stochastic's %K. Taking a threeperiod moving average of each %K will result in the line that is used for a signal.
For more insight, read Getting To Know Oscillators  Part 3: Stochastics or Support, Resistance, Stochastics, and EMA

What are the best technical indicators to complement the Stochastic Oscillator?
Explore the function of the stochastic oscillator indicator, and discover other technical indicators traders use to complement ... Read Answer >> 
What is the difference between Stochastic Oscillator & Stochastic Momentum Index?
Discover how the stochastic oscillator and the Stochastic Momentum Index differ and why the latter is considered a more refined ... Read Answer >> 
Would a slow stochastic be effective in day trading?
Given the hundreds of indicators that are available to traders, finding the appropriate technical tools to use in day trading ... Read Answer >> 
How do I use Stochastic Oscillator to create a forex trading strategy?
Learn about the stochastic oscillator and how to it is used to create an effective forex trade strategy, including how to ... Read Answer >> 
How does a swing trader use the stochastic oscillator?
Learn how the stochastic oscillator is used as a momentum indicator in swing trading, and understand how the oscillator is ... Read Answer >> 
Why is the Stochastic Oscillator important for traders and analysts?
Understand how and why analysts and traders consider the stochastic oscillator a useful tool for anticipating trend exhaustion ... Read Answer >>

Trading
Triple Screen Trading System  Part 5
Stochastics can be very effective as the second screen in this threepart system. Find out how to use this popular oscillator. 
Trading
Do You Have The Right Settings On Your Stochastic?
Use these helpful tips to unlock Stochastics' full potential. 
Investing
Stochastics: An Accurate Buy And Sell Indicator
Find out how stochastics are used to create buy and sell signals for traders. 
Trading
Combined Forces Power Forex Snap Strategy
Stochastic and MACD oscillators can help isolate greater opportunities in rangebound markets. 
Trading
4 DoubleCross Buy Signs
Will the double crossover on MACD and Stochastic indicators trigger a move higher? 
Trading
How Do You Use the Stochastic Oscillator?
A stochastic oscillator is a technical momentum indicator that compares a security's closing price to its price range over a given time period. 
Trading
MACD And Stochastic: A DoubleCross Strategy
Two indicators are usually better than one. Find out how this pairing can enhance your trading. 
Trading
MACD And Stochastic: A DoubleCross Strategy
The stochastic oscillator and the moving average convergence divergence (MACD) are two indicators that work well together. 
Investing
Premier Stochastic Oscillator Explained
This oscillator has been used since the 1950s by traders and investors to anticipate areas where the market may change direction. 
Trading
How To Best Analyze Relative Strength
Relative strength indicators measure performance between similar instruments, uncovering opportunities that can translate into reliable profits.

Stochastic Volatility  SV
A statistical method in mathematical finance in which volatility ... 
Stochastic Modeling
A method of financial modeling in which one or more variables ... 
StochRSI
An indicator used in technical analysis that ranges between zero ... 
Williams %R
In technical analysis, this is a momentum indicator measuring ... 
Signal Line
A moving average plotted alongside a technical indicator and ... 
Technical Indicator
Any class of metrics whose value is derived from generic price ...