Trade cards are the multicoloured ones that we generally seem to call "upgrades". You can purchase them (from the tableau) or play them from your hand during any phase - as you can with any card. Phase only matters for which cards are "scored". For this reason you tend to play or purchase cards of the current phase, but this is not always the case - sometimes you need to clear your hand to pick up a card that has just appeared on the tableau (and which you may not be able to afford or want to pay for currently).
As others have said, you can buy any available card in any phase, and you can play any card from your hand in any phase.
Usually, you will be playing cards in their own phase - e.g. workers in the worker phase, etc - because you'll see the quickest return on them. If you play/buy a worker card in the building phase, for example, you'll have to wait through the building phase, the aristo phase, the trading/upgrade phase, and then the next worker phase before he'll earn you any money. In the meantime, you could've been using the money you spent on him on other things.
But there are times when it's useful to buy/play a card during the "wrong" phase.