I have a basic vintage road bike. Is there a difference between the rear and front wheels?

If I replace the rear wheel, do I need to by a wheel specific for the rear of the bike? or are wheels generic and can be placed at either the front or rear of the bike?

Can I modify a front wheel to become a back wheel?

The front and rear wheels are not interchangeable. You cannot modify a front wheel to become a back wheel. Most bikes cannot swap 27" and 700C wheels due to the brake reach.

Most modern wheels have 7speed (126mm) or 8/9/10 speed (130mm) widths for the rear hub. This means that (1) you'll have to have the frame modified to accept the wider wheel, and (2) you'll have to modify your drivetrain to use the aditional gearing.

I suggest finding a used bike at a yard sale or flea market with the same sized wheels as your current bike and swapping the wheels. You should be able to find one for under $20.

No you cannot use a front wheel as a back wheel.

You need a hub which has threading on so you can screw on a freewheel, or get a modern hub with a Freehub so you can fit on a modern cassette.

You will be able to re-use the rim though, but I would assume you would need to replace the spokes as most likely the hub's flange will be a different size, and so the spokes will need to be longer/shorter.

I would suggest getting 700C wheels though. They may look a little odd on a vintage bike, but you have many, many more choices on tyres available to you.

Bikes are usually symmetrical, there is an easy way to find out though if you are worried. Place some tape on the floor and roll your bike forward one revolution of the tire. Measure the distance. Do this for front and back. If they are the same, then your wheels are the same size.

If it's an old bike it will have 27" wheels, and those are getting hard to find new. Front wheels are different from rear wheels as they need different hubs.

The rims will be the same, but the wheels are different, just take a look at them.