Weird Heading 1 style behavior

I'm having trouble figuring out why my Heading 1 style is misbehaving.  I have only 1 Heading 1 style, but my document has 2 sections. I'm using 2 sections, so that I can have different Page Headers for pages in section 2.

But for my paragraph numbering, I have only one Heading 1 style.

Problem:  If I click a level one paragraph title, and make it Heading 1 style, it works fine, througout that section.  However, when I get to section 2, and click on a level1 title, and apply the same Heading 1 style, it's different from the one in section 1.

Further complicating things, IF I modify the style, to correct the problem in Section 1, THEN the section one level 1 headings are affected.

Example:

Section 1:

1.0    Paragraph 1 title

Section2:

4.0                                    Paragraph 4 title

IF I fix the heading style in Section two, section 1 Level 1 Heading is messed up. 

Example

Section 1:

1.0                                 Paragraph 1 title

Section 2:

2.0  Paragraph 2 title

Aren't Heading styles the same across multiple sections?

Are there section properties that interfere or conflict with styles?  

Is it possible to have a global style that applies across multiple sections?

What causes this? and What is the solution?