Is it true that donations only make a difference to your tax refund if they total $200/250 or more per year?

No, not in Australia. There's no minimum deduction. But, of course, you more you donate, the higher your deduction, the less your taxable income becomes and subsequently you get a proportionally higher tax refund or lower tax payable.

Donations of $2 or more to eligible gift recipients are tax deductible. The organisation must be on the ATO list of EGR and donations must be more than $2. If you donate to, say a foreign organisation that is not on the list, you can't get a deduction. For instance, you donate $1000 to a US organisation, no deduction is allowed. The ATO has a system to indentify abnormally high donations amount in the tax return & may write to ask you for details of what made up.

Is this an Australian question?

If so Miss Schlonky is correct - and maybe Blah's comment is more relevant to other jurisdiction??

It is correct that donations by themselves cannot create a tax loss, but you don't need to itemise what makes up your, say, $10,000 total annual donations - until the ATO ring and ask you (or write and ask you).