I'm trying to find a certain style of font but I'm not sure what to search for.
It's the same font as in the Vox News logo.
Also something like the Harriet Display family.
This font belongs to a roman family called Transition Romans or Transitional Romans. The name comes from the transition in time and shape between the ancient and modern romans. All romans types has common points, the difference between them is how they are made.
The Vox logo is an example of a "fat face" typeface–an ultra-bold Didone typeface, a style that was popular from the early nineteenth century. (Bold type didn't exist in the eighteenth century.) The huge ball terminals on the 'x' are very nineteenth century too. Something like Sybarite or Stilla would be what you want, but contact me if you know you want something else. The key is that this font is not just bold but ultra-bold: it's bolder than a font simply designed as a bold complement to a body text font would be. (Obviously the connection between characters is custom–this is a customised italic font, not a script typeface.)
I found Playfair Display's Bold Italics to be eerily similar to Vox's brand font. Note:
V follows the same pattern of thick and thin lines.
o is slanted at a similar angle. Although the original is thicker.
X has the end-circles. With similar thick and thin lines.
I'm aware it's not the same. A great inspiration, nonetheless.
Disclaimer: I'm not a Typography expert.