While both ways will give you the correct output, the more correct way would be to use a single font-family to group all the different variants of weights and styles. It's the same way you use system fonts (from 'Arial' down to 'sans-serif') and, in fact, if you use Google fonts to load Raleway you would be using the single font family route.
Let's outline several reasons why this is the correct method.
It reduces CSS complexity an, ultimately, file size
Having a single font-family means you can define an entire containing element with the font family, and only certain elements with different weight/styles. Take the following, for example:
html {
font-family: Raleway;
}
.bold {
font-weight: 700;
}
.italic {
font-style: italic;
}
.footer {
font-family: Arial;
}
<p>I'm raleway font, <span class="bold">and I'm raleway bold</span></p>
<div class="bold italic">I'm Raleway Bold Italic!</div>
<div class= footer>I'm <span class="bold">Arial Bold,</span> w/ the same class!</div>
Notice how nice and consice this CSS is. We didn't need to specify "RalewayBold" as the font-family for .bold, nor "RalewayItalic" for our .italic. Infact, we don't even need to specify a bold & italic variant, since our classes will simply work. Further, if .bold is inside our .footer, it will be bold Arial and not Raleway, because it simply inherits Arial from the footer container.
It's the way the browser does it.
The above is essentially how the browser internal stylesheet defines fonts by using minimal styles and the inherent cascading nature of CSS.
It's the way the industry does and has done it.
The biggest web properties, applications and publishers all do it this way. Google, Facebook, NYT, ESPN, etc. all define and use fonts in this manner.
Not only that, but user interfaces before the CSS or even the internet specify single font-families and choose variants based on different specification of weight and style. Load Microsoft Word, KeyNote, Google Docs, even an old late 1990s WordPerfect and open the font drop-down; You'll see the font-family name "Arial" listed; not "Arial" followed by "Arial Bold" followed by "Arial Italic" etc.
Just load from Google Fonts.
If you load Raleway from the free webfonts repository on Google Fonts, you'll see Raleway is defined with a single family name:
https://fonts.googleapis.com/css?family=Raleway:400,400italic,500,500italic,700,700italic
@font-face {
font-family: 'Raleway';
font-style: normal;
font-weight: 400;
src: url(https://...Raleway-Regular.woff2) format('woff2');
}
@font-face {
font-family: 'Raleway';
font-style: normal;
font-weight: 700;
src: url(https://...Raleway-Bold.woff2) format('woff2');
}
@font-face {
font-family: 'Raleway';
font-style: italic;
font-weight: 500;
src: url(https://...Raleway-MediumItalic.woff2) format('woff2');
}
@font-face {
font-family: 'italic';
font-style: normal;
font-weight: 700;
src: url(https://...Raleway-BoldItalic.woff2) format('woff2');
}