Is it true that the difference between Convertible and Warrants is that:
Convertibles are redeemed at nominal value or convertible value whichever is higher, but in Warrants on redemption date investors redeem at nominal value plus the right of new shares at future date at a fixed price.
In Warrants investor will receive both nominal value + new shares on fixed price
What you have written is correct. (Except that the warrants give the right to buy new shares at a fixed price on a future date, but the future date is usually before the redemption date.)