Budgeting vs. Tracking: What's the Difference?

Budgeting is what happens before you receive and spend your paycheck. All you're doing is creating a financial plan for the pay period (or, as I like to call it, "spending period").
It's like you've just filled up your tank with gas, plugged your destination into the GPS, and chosen which route to take. In addition to a giving you destination, a budget gives you turn-by-turn directions; for instance, if you've decided to spend $250 on debt repayment, then you're not spending that $250 on new clothes from Banana Republic. A budget causes you to decide things ahead of time based on what's important to you.
Tracking is seeing how closely you're following your plan. If budgeting is the GPS system guiding you, tracking can show up as miles driven, landmarks seen, etc. Tracking merely reveals data.
All budgeting requires tracking but tracking can't be considered budgeting on its own. There's no overarching plan to dictate it. It's just spending, saving, investing, etc.
Why on Earth does this matter?
If you're budgeting, you're being more intentional with your money and life.
You're basically saying, "I'm doing this, this, this, and this" before life happens. If you're setting a B.H.A.G. to get out of debt or build an emergency fund, this is crucial. Taking directional ownership gets you to your goal way quicker than just dilly-dallying.
Even if you don't have a set goal, you're deciding what's right for you and acting upon it before anything (or anyone) gets in the way. You're choosing you.
You also get a weird sense of freedom because your cognitive load is so much less. For seven years, I didn't eat meat or poultry. Going out to dinner was great because, on a restricted diet, I knew exactly what to order because I wasn't overwhelmed with choices. I had less decision fatigue.
So while it may seem really annoying to do a budget (especially in the beginning), the increased emotional and mental bandwidth you get in return is priceless.