First of all, you should be checking if x or y is less than the respective number, not greater than.

Next, your while loops aren't written properly; you are simply increasing x and y every frame; the while loops do nothing. For each one, change it to:

1. while (x < 649) {
   
2.   x = x + 1;
3. }

Now, you should see something different; but all of the animation is happening on the first frame.
Instead of while loops, now, use if statements:

1. if (x < 649) {
   
2.   x = x + 1;
3. }

Notes:

x and y typically refer to x and y coordinates, not two different x coordinates.
Instead, I would recommend using x1 and x2.

You don't need all of your drawing statements in setup(); they are called in draw() anyway.

Instead of using x = x + 1;, you can use x += 1;, or even better, x ++;; they all do the same thing.

Final Code:

1. float x1 = 100;
2. float x2 = -100;
3. void setup() {
4.   size(700, 150);
5. }
6. void draw() {
7.   background(200);
8.   fill(0, 250, 200, 200);
9.   rect(x1, 50, 50, 50);
10.  
11.   if(x1 < 649) x1 ++;
12.  
13.   fill(0, 0, 255, 250);
14.   rect(x2, 50, 50, 50);
15.  
16.   if(x2 < 100) x2 ++;
17. }