You never use the variable t2 which you need for the full sphere also the z and y coordinates : y goes north>south pole and x/z go round equator.

The following sketch demonstrates the solution

1. int m1=20, m2=20; // number of steps  
2. float t=PI/m1; // angle 1  
3. float t2=2*PI/m2; // angle 2   
4. float x,y,z;
5. float xm=0;
6. float ym=0;
7. float zm=-160;
8. float r = 140;
9. void setup() {
10.   size(300,300, P3D);
11.   xm = width/2;
12.   ym = height/2;
13. }
14. void draw() {
15.   background(255);
16.   for(int i=1; i<=m1+1; i++) {        
17.     for(int j=1; j<=m2+1; j++) {           
18.       x=xm+r*sin(t*i)*cos(t2*j);           
19.       y=ym+r*cos(t*i);
20.       z=zm+r*sin(t*i)*sin(t2*j);           
21.       point(x,y,z);
22.     }
23.   }
24. }

I don't work with P3D but with my own 3d-area. boxes, circles, ... work wonderful but with the sphere it seems to have a problem. when I copy my code into a P3D-sketch it also works fine

Is 3d-area is a library you have created?

If it works in P3D but not in 3d-area then it is probably because the 2 graphics modes are using different coordinate systems. In P3D X and Y and in the plane of the screen with positive X going left to right and positive Y going top to bottom. Z=0 is a point on the screen with negative Z going into the screen and positive Z coming out of the screen. When I look at your calculations it seems to suggest a different coordinate system.

There I work with z-axis going into the screen and x going right and y going down. So that could be my fault.

That's the same as P3D & OpenGL apart from the z axis direction but since a sphere is symmetrical about the Z axis then there is no effective difference.

Compare the code you posted originally and compare that to the code I posted particularly the calculation of x,y,z you will see they are significantly different in particular the y/z calculations are swapped.

If you are not using P3D then what are you using for instance in setup() you should have a method call to size e.g.

1. size(width, height, ???);

what do you have for ???

Processing has 4 different graphic display types P2D, JAVA2D, P3D and OPENGL. The first 2 are for 2D display purposes and uses x,y coordinates. The last 2 can be used for both 2D and 3D displays and so you have x,y,z coordinates.
If you don't specify which one you want Processing will use JAVA2D so although you don't have a third value yoour statement

size(300,300);

is the same as

size(300,300, JAVA2D);

I don't know why you have taken the approach you have to drawing a 3D sphere using a 2D renderer but you have 2 possible sources of error

1. Calculation of the sphere coordinates
2. transformation of the x,y,z coordinates to 2D

If you are serious about doing something in 3D I suggest you learn how to use P3D and OPENGL modes as it will do the transformation to 2D for you, including perspective. It you want to avoid the perspective effect then you can use the ortho() method provided by Processing.