There is no difference between your two examples. One can include the word "that", or one can exclude it. It is more likely to be included in writing than in speech. The more formal the context, the more likely the "that" is to be included.
She said that they had gone out last night.
She said they had gone out last night.
Both are correct, the latter less formal.
She said that he worked in a bank.
She said he worked in a bank.
Both are correct, the latter less formal.
Here are some other examples where "that" is omitted informally:
- She said (that) she knew.
- You said (that) I could.
- They said (that) they didn't want to leave.
- We said (that) we would be there.
- He said (that) he didn't like it.
- You said (that) you'd seen it.
It can also be omitted in contexts unrelated to reported speech.
- I told him (that) I liked it.
- She knew (that) we were there.
- I thought (that) I knew you.
- I'm glad (that) I found you.