1. It appears that there has been a mistake.

2. There appears to have been a mistake.

3. It happened that she was out when we called.

4. She happened to be out when we called.

5. It chanced (that) they were staying at the same hotel.

6. They chanced to be staying at the same hotel.
---------------------------------
Is each pair the same and grammatical?

1 answer

Each pair means the same thing, but 3 is wordy, and 5 and 6 are awkward. I've never heard anyone use the phrasing in 5 or 6.