I'm not a native English speaker, hence I'm a little confused here. I want to know the difference between the two and also correct me if I'm saying it wrong here "It's turns out to be a conspiracy against him." "It turns out that it was a conspiracy against him." I can't figure out the differene, I have been trying to find the answers, I even get them but they aren't satisfactory.
- "turn out" as an intransitive verb (usually followed by "to be") means "prove to be" e.g. "His book turned out to be a failure".
- "turn out" (not followed by "to be") means "to end up", "to result". e.g. "His painting turned out beautifully.", "Don't worry, everything will turn out fine"
Sometimes "turn out" and "turn out to be" are interchangeable.
In addition, you have the idiom "it turns/turned out (that)" which means "happen", "end up" e.g.
"After it was all over, it turned out that both of us were pleased with the bargain" TFD ,
"As it turned out, it was Joe who had told her everything."
turn out that ... plus a that clause, while turn out to be plus a phrase, which is kinda the obvious difference. Just like the previous explanation, sometimes turn out to be and turn out that share the same meaning and even sometime with the different usage they actually mean the same thing. e.g. It turns out that it is a good method. It turns out to be a good method. BTW. The first sentence in your question, It's turns out ... is probably wrong.
It turns out to be a conspiracy against him,
"it" is a pronoun standing for the thing that turned out to be the conspiracy.
It turns out that there was a conspiracy against him,
"it" is a dummy pronoun that doesn't stand for anything. Thus, if you use the first form, you need to have an antecedent for "it".