It almost certainly was Riddle’s diary that she’d left at the Burrow.
Though it’s not mentioned whether Ginny typically kept a diary before or since being given Tom’s, it’s very likely the diary she wanted to go back for was that one. It’s unlikely that the mention of Ginny being upset at leaving a diary behind was coincidence, when her having that specific diary becomes very important later on. Also, she was very attached to Tom’s diary when she had it, she considered him like a friend, so it’s likely she’d be very unwilling to leave it behind, even for a bit.
“It’s very boring, having to listen to the silly little troubles of an eleven-year-old girl,’ he went on. ‘But I was patient. I wrote back, I was sympathetic, I was kind. Ginny simply loved me. No one’s ever understood me like you, Tom … I’m so glad I’ve got this diary to confide in … It’s like having a friend I can carry round in my pocket …”
- Harry Potter and the Chamber of Secrets, Chapter 17 (The Heir of Slytherin)
It being Tom’s diary would explain why she was unwilling to part with it even for a short amount of time, and just have her parents owl it to her at Hogwarts rather than make them late - she was very attached to it, and additionally, it had a way of making people unnaturally interested in it from first contact. Harry found it soaking wet in toilet water, and knew from looking at it that it was blank.
“Harry peeled the wet pages apart. They were completely blank. There wasn’t the faintest trace of writing on any of them, not even ‘Auntie Mabel’s birthday’, or ‘dentist, half past three’.”
- Harry Potter and the Chamber of Secrets, Chapter 13 (The Very Secret Diary)
Despite it being blank and soaked in toilet water, Harry takes it with him, for no logical reason.
“Well, it’s not much use to you,’ said Ron. He dropped his voice. ‘Fifty points if you can get it through Myrtle’s nose.’
Harry, however, pocketed it.”
- Harry Potter and the Chamber of Secrets, Chapter 13 (The Very Secret Diary)
After that, Harry still kept picking the diary up to read it despite already knowing it was blank.
“Harry couldn’t explain, even to himself, why he didn’t just throw Riddle’s diary away. The fact was that even though he knew the diary was blank, he kept absent-mindedly picking it up and turning the pages, as though it was a story he wanted to finish.”
- Harry Potter and the Chamber of Secrets, Chapter 13 (The Very Secret Diary)
Harry had no clear reason to be carrying this diary and yet he did until Ginny panicked and stole it back. Ginny had far more reason to feel connected with it, since she considered it her diary with a friend inside it, so she’d be likely even more reluctant to part with it for any reason.