I'm really not so familiar with Strategy Tester. I've tried it in the past for a very short time. I think it is something like a "player" that plays the history data and you can watch it (if you have missed watching it in real) and can set indicators and you can trade in the same way as it is a demo account. It can play the market with different speed, so you can make it faster, when the market is slow and you are inpatient to wait it to develop. I'm not sure if it can trade experts on past time as a backester.
FSB is very different in design and purpose. In FSB you spend your time in developing a strategy of indicators. The program backests this strategy in real time and you see the result of the historical test. When you created, tested and analyzed the strategy, you can export it as an Expert Advisor and trade it via MetaTrader. FSB has also automatic strategy generator, optimizer and many other tools for evaluation of a strategy.
I'n not sure, but the Forex Tester may be more suitable for the first steps in the Fx trading. You can use it to play on the market even on Saturday and Sunday. However I don't see much value in it for an intermediate or seasoned fx trader.
On the other hand, FSB requires some knowledge for the market and indicators.
Fortunately, I'll start a new video series for trading with MT and creating EAs with FSB next week. I'll cover the whole a bunch of stuff with greater details. You may find it useful.