I heard someone singing
but I haven't seen
I heard someone that is singing
Is it the same as the first one?
I heard that someone is singing
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The first two sentences mean the same thing. Note that many people will prefer "I heard someone who is singing," since "who" refers to a person. You seldom hear this expanded version though because the "that/who is" is unnecessary and people will just say the shorter version "I heard someone singing."
Your third sentence means something completely different: "I heard that..." means that you have heard about something rather than hearing it directly. This could even refer to something that is going to happen in the future, since reported speech can backshift the reported action from the future to the present.
Q: What is the entertainment going to be at the party tonight?
A: I heard that someone is singing.
So unlike in the first sentence, where you directly heard a person who is singing, in this case you haven't directly heard anyone singing (the singing won't even happen until tonight). Instead, you have heard someone tell you that someone will be singing tonight.