Packed weight is the weight of everything that comes in your tent's box when you buy it.
Trail weight is the manufacturer's minimum weight for a barebones setup. Trail weight excludes "extra" items like stuff sacks, pole repair kits, patch kits, etc.
Here's a simple chart showing the difference between trail weight and packed weight:
Stakes and stuff sacks have a 50/50 chance of being included in trail weight.
Guy lines and repair kits aren't usually included by most manufacturers.
Some manufacturers choose to include them; others say they're optional and choose not to count them in the trail weight.
Trail Weight Isn't A Standard Measurement
You have to be careful whenever you see trail weight listed.
Every manufacturer can decide for themselves what to include in their stated trail weight.
This means they can make the trail weight much lower than what you'll actually experience when you're using the gear.
You should always go with the packed weight when you're planning how much your gear will weigh.