Here is the power supply that you have. Antec VP450

`Features
• 450 watts of Continuous Power • ATX12V version 2.3 compliant
• Dual +12V rails ensure greater system stability
...........
The spec says "DUAL 12V rails"
If as you suggest, the power supply has just Two yellow(12V) wires, then it should be blatantly obvious that they are "colour coded" differently to show you they belong to the same rail, they're part of the dual rail. And even if they were not "colour coded". If they were only two(as you suggest) then obviously those are the two mentioned in the Specification, which says 12V dual rail!
This tomshardware forum link mentions something on it, but this post on overclockers forum is far more comprehensive.
To quote from it
What is "multiple +12V rails", really?
In most cases, multiple +12V rails are actually just a single +12V source just split up
into multiple +12V outputs each with a limited output capability.
And
Ok... What's the bottom line?
The bottom line is, for 99% of the folks out there single vs. multiple
+12V rails is a NON ISSUE. It's something that has been hyped up by marketing folks on BOTH SIDES of the fence. Too often we see
mis-prioritized requests for PSU advice: Asking "what single +12V rail
PSU should I get" when the person isn't even running SLI! Unless
you're running a plethora of Peltiers in your machine, it should be a
non-issue assuming that the PSU has all of the connectors your machine
requires and there are no need for "splitters" (see Example 1 in the
previous bullet point).
That might not answer everything but it answers a bit.
Edit
The above may be incorrect.. I was going by what those forums had said.. I don't think I personally have used a PSU with dual 12V.. A commenter has said that most of the time, when a PSU has dual 12V, then they are two different rails.
A commenter differs with the tomshardware link and said it's not a non-issue, as that link says, but far from it, it's a big issue.. He writes "ITS A BIG ISSUE. Say for example you have a hard drive enclosure that needs 2 power connectors attached. if you connect 12v from one rail, and 12v connector from the separate rail (most that say dual, are in fact, 2 separate rails), you can do serious hard to the drive cage, and likely destroy and hard drives in it! – warath-coder"
I'll adjust this answer if I look into it more. But for now i'm on the fence. And it's perhaps better to proceed with caution.. going with what warath said. The answer from Damon mentions what might be a way to test if two wires are on the same rail.