Regarding HSA contributions, are contributions by payroll deduction the same as personal contributions?

Under the tax code, what is really happening with your employer is that you are agreeing to a voluntary salary reduction and your employer is making the contribution for you (plus any employer match).  So all workplace contributions are employer contributions and are reported on your W-2.

Personal contributions are only those made directly to the HSA bank out of pocket, and not through payroll deduction. 

In a word, "No". As Opus says, HSA contributions can be "employer" HSA contributions (even if you think you're making the deferral) or "personal" contributions (those you make directly to the HSA not through your employer).

The confusing thing is that these two types of contributions are treated quite differently. The "employer" contributions don't appear on your 1040 (but they do appear on form 8889) because this amount is removed from your Wages before your W-2 is even printed, while the personal contributions appear on line 13 of Schedule 1 (1040). They are also handled differently when an excess contribution is made, but I won't describe that unless you want me to.