If you want to understand why the TPP is the way it is, look at the Japanese domestic auto market. Their tariff on imported cars is zero, but somehow foreign cars almost never make it to market. Maybe they fail a safety inspection at the port. Maybe there are local registration fees that mysteriously appear and driven up the cost. Maybe the Japanese-run local affiliate is really really slow to move inventory into the stores, or sends a shipment back.
And this does not even get into the barriers that foreign manufacturers face in trying to set up local manufacturing in Japan. There are a million ways a government can stall an investment or construction project if they want to.
These are collectively known as "non-tariff trade barriers" or NTBs. They are the weapon of choice these days to restrict trade, so modern trade agreements have to spend many of their pages addressing NTBs.
To name another example that might resonate with HN, consider the local restrictions that a nation might put on data. For example, a nation might require that any company serving its citizens build data centers within its borders and keep all data within those data centers. That would make it extremely difficult for any but the largest U.S. tech firms to enter foreign markets. That's not a tariff but would obviously slow down trade in Internet services.
As I understand it, TPP will have language to allow data to cross borders.