SEO of <span> in <h1> header

There is no difference between your two examples. However, if your differently-coloured word is an important keyword, you may consider using the <em> or <strong> tag to suggest emphasis. CSS can take care of the styling:

h1 em {
  font-style: normal;
  color: #123456;
}

Emphasis usually boosts SEO a little, although I don't know how much difference it makes when inside a header. Regardless, it makes for some simpler and more semantic HTML which is always a bonus.

There should be no difference. The <span> element has no semantic meaning whatsoever.