It is definitely common with both designs using a combination of typefaces (typically 2; one for headers and one for body) , and sometimes only 1 typeface. I can't say I have found specific research pointing whether one is better than the other, I guess it depends on the style you are trying to convey (the brand image of the company might play an important role there too; sometimes there is also already existing brand guidelines / style guides in place which needs to be followed).

Here are however some links that might be useful:

[7 Golden Rules of Combining Fonts for Mobile][1]

 1. Make it readable
 2. Establish a Visual Hierarchy
 3. Consider the Audience
 4. Create Contrast
 5. Use Fonts from the Same Family or Designer
 6. Limit the Number of Fonts
 7. Don’t Forget to Test It Out

[Best Practices for Combining Typefaces (Smashing Magazine)][2]:

 - Try matching a Sans-Serif title type with a Serif body type
 - Avoid similar classifications (don't use 2 slab typefaces or 2 condensed typefaces)
 - Assign distinct roles to each typeface/font
 - Contrast font weights
 - Create a variety of typographic colors
 - Don't mix moods
 - Contrast distinct with neutral (rather than with another distinctive
   font)
 - Avoid combinations that are too disparate (e.g. narrow & expanded)
 - Keep things simple (try just 2 typefaces)
 - Vary point sizes

There's also the more practical side (with code examples for web) from [Donny Truong (I specifically link to the part with combining typefaces, but the whole book is recommended)][3].


  [1]: https://webdesignledger.com/7-golden-rules-mobile-fonts/
  [2]: http://www.smashingmagazine.com/2010/11/04/best-practices-of-combining-typefaces/
  [3]: https://prowebtype.com/choosing-headings/#combiningtypefaces