No. If the bank say it doesn't, they may have removed the product. But you do need to be clear about the 2 distinct type of products in your mind yourself, to be able to ask them the right questions to be absolutely sure. Why not describe the product you want, and ask them if they have it? If ICICI don't, it's such a common product that there would be any number of other banks offering it, if you must have it.
If you ask me, you're much better off with the Flexi FD product than with the auto sweep-out - sweep-in thing. It allows you more control over your own money, and potentially could generate more income for you as well. And in the days of netbanking, it requires only minutes more of your time per year!
Believe me, I'm talking from years of experience. I like to be as lazy myself as I can afford, but I'd much rather benefit from it myself than offering it to somebody else (like a bank)!
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