A Trade Embargo cancels any trade routes that you may have with that race, including trade routes they may have established.  And, obviously, it prevents them from opening new trade routes with your planets.

Economic treaties are traded just like anything else.  When you give them an economic treaty for something (usually one of their treaties) they get some bonus income based on how well your economy is doing.  When they give you an economic treaty, you get a bonus income.  This isn't deducted from anyone's income, it's on top of what you get from tax, income and trade routes.