Cap and trade is fundamentally different from offsets in that there is a central authority who decides precisely what caps every company gets before trading starts, so every transaction which increases one company's cap by 1 ton is guaranteed to decrease another's.
Offsets are a decentralized attempt to quantify how various actions would lower the world's carbon output compared to some estimate of what would happen otherwise. The cheapest offsets prey on this ambiguity in the various ways the article suggestions.
The other big difference is that cap and trade is mandatory while offsets are optional. There is so little offset-buying happening now that the markets are artificially cheap. Companies currently claiming to be "carbon neutral" would certainly be unable to afford doing so if it was required of every company (similar to if the "cap" was universally zero carbon, a clear non-starter today).
Even if everyone involved operated with good faith, even accounting accurately for the co2 externalities accurately is very difficult, and you can be sure a huge percentage of people will not be acting in good faith.