Like they say, a rose by any other name is still a rose. There will come a time that khomr will be given (called) a different name so that it can be consumed by the people who are oblivious.
Point is... Whether or not it is qard or wadiah, we need to look at the essence of it, the fundamentals of the transaction.
In wadiah, you get back the item you give, not an equivalent/substitute. In qard, you can lend out your motorbike and the guy can return to you a similar/equivalent bike. In wadiah, it must be the same bike that is returned. In terms of money, it should be the same bank notes (same serial number).
Obviously, there are other related rules, but in this regard, to establish whether it is qard or wadiah, we can look at the object.
I quote below.
Syaikh Muhammad bin Shalih Al-‘Utsaimin rahimahullah ditanya, sebagian bank memberikan hadiah kepada nasabah yang cuma menyimpan uang saja tanpa ambil bunga, apakah hadiah tersebut boleh dimanfaatkan oleh nasabah?
Syaikh rahimahullah menjelaskan, “Engkau sudah tahu bahwa menyimpan beberapa dirham di bank itu bukan disebut wadi’ah (menitip), namun akad sejatinya adalah qardh (meminjamkan). Yang disebutkan oleh orang-orang bahwa akad tersebut adalah wadi’ah itu keliru. Jika engkau menyerahkan uang pada bank, apakah bank itu menjaga uang tadi sebagaimana adanya, sampai nanti diminta kembali juga bentuknya seperti itu ataukah bank menggunakan uang tadi terlebih dahulu? Tentu bank akan masukkan dalam tabungan dan akan menggunakannya. Kesimpulannya, hakikat akadnya itu qardh (meminjamkan), bukan wadi’ah (menitipkan). Kalau transaksinya adalah meminjamkan, maka orang yang memberikan pinjaman (kreditor) tidak boleh mengambil keuntungan sama sekali dari transaksi tersebut, tidak boleh menerima hadiah dan lainnya. Hadiah barulah bisa dimanfaatkan setelah utang itu lunas (selama bukan syarat yang ditetapkan di awal, pen.).
Sumber
https://rumaysho.com/24234-titipan-dan-pinj...dan-ariyah.html(note: I think "pen." at the end of the above quote is either the writer/penulis or translator/penerjemah. Who knows, not really familiar with these terminologies)
It is not the classical wadiah as in you keep your item with other person. It is wadiah yad damanah. This a contract introduced by scholars through their ijtihad. What does it mean?
-You intend to keep you money with the bank. This is wadiah part.
-At the same time you authorize bank to use your money, why? Because that's how banking system work, that's how the accounting, any money deposited will be put in pooled account.
-Due to the money being used, bank shall provide guarantee to return principal amount upon request (withdrawal)
What sheikh Utsaimin said is his ijtihad.... which one of so many other scholars ijtihad. You are free to follow which opinion you are comfortable with.