Hey there! Welcome to Chicken Smoothie c:
For player-player trades, you can choose to send a trade or a suggestion. If it's a trade, your trading partner can accept/edit/cancel it. If it's a suggestion, your trading partner can only edit or cancel it. You can also send a message along with your trade/suggestion so it'll be easier to negotiate with your trading partner. Unlike FR, you can add your partner pets/items/C$ (CS currency that you can buy using real money) to your trade. (assuming they have their stuff unlocked)
If you don't understand this explanation/have more questions, please don't hesitate to PM me
Here are some useful links that I'd recommend checking out
Adopt a Newbie General Helper Adoption Alliance (get free pets)
Newbie Guide&IndexMust-Read Topic for Newbies