There is no confusion.
When one is a warrant holder, there is a (indirect) position in shares, but there is nothing to sell.
There is no market for the warrants so the value can't be cashed.
Once exercised, the shares can be sold and (often) will be sold at least partially as one has to come up with cash to pay for exercising.
Also one can realize the profits from having held warrants by selling shares.
Exercising of warrants will lead to an additional supply of shares.