"In effect" means that while something is different from another thing, their effects are very similar or identical.
"In fact" means something is accurate. It's fact. It's not just the effect, but the FACT. With the right context, this can be synonymous with "in effect," but absent that context, it's not. Without context forcing them to be synonymous, "in effect" tends to be a statement about something that is covert and/or indirect, while "in fact" is more firm about what was going on.
-In effect, the two systems are identical.
-In fact, the two systems are identical.
First sentence: the two systems arrive at the same place/give the same results, despite using different means to get there. Second sentence: the two systems are either exactly the same, or exactly the same in function with a few details changed. (E.g., two computer programs that have identical functions, but slightly different user interfaces.)
-His wife had, in effect, run the government for the past six months.
-His wife had, in fact, run the government for the past six months.
First: his wife was the power behind the throne, making suggestions or giving other people covert instructions, but not actually wielding power overtly. Second: His wife was giving orders and telling people what to do.
-In effect, this means we’ll all have to work longer hours for the same pay.
-In fact, this means we’ll all have to work longer hours for the same pay.
First: The situation is obfuscated so that you have to dig around to realize that the effect of [whatever prompted this sentence] will result in longer hours. Second: It's out in the open. The situation requires longer hours, and no one's getting any extra money for it.