Question: I am writing some equations where I need to distinguish between bold and non-bold quantities. However, for some symbols there is barely any difference when I just use `\mathbf` or `\boldsymbol`. Is there a way to 'increase the boldness' of math symbols?

Answer: 
In comments it is stated that you are using `mathptmx` this is an old package targetting the fonts available in early PostScript laser printers. It has no support for bold math.

```
\documentclass{article}

\usepackage{mathptmx}

\begin{document}

 $\alpha$ \boldmath  $\alpha$
\end{document}

```

produces the warning

```
Package mathptmx Warning: There are no bold math fonts on input line 7.

```

If you want a Times-like math font that has support for bold symbols use for example `newtxmath` or `stix2`.

[![enter image description here](https://i.stack.imgur.com/3vGrO.png)](https://i.stack.imgur.com/3vGrO.png)

```
\documentclass{article}

\usepackage{newtxtext,newtxmath}

\begin{document}

 $\alpha$ \boldmath  $\alpha$
\end{document}

```
In `unicode-math`, you can declare a bold math version and use `\boldsymbol`. XITS Math comes with one, and `\setmathfont{XITS Math}` will load it automatically for `\boldsymbol`, `\boldmath` and `\mathversion{bold}`. You could also embolden a math font with `FakeBold`, as in:

```
\usepackage{unicode-math}
\setmainfont{TeX Gyre Termes}
\setmathfont{TeX Gyre Termes Math}
\setmathfont{TeX Gyre Termes Math}[
   version = bold,
   FakeBold = 1.2 ]

```

The one disadvantage of this is that, as of 2021, you cannot combine `version=` and `range=`.

In legacy 8-bit TeX, you normally want to load a newer font package that comes in a bold version. You can also declare a bold version for any math alphabet with e.g. `\SetMathAlphabet`, or a bold version of any math symbol font with `\SetSymbolFont` (and then optionally use the symbol font as a math alphabet as well, with `\DeclareSymbolFontAlphabet`). See [The LaTeX Font Selection Guide](https://www.latex-project.org/help/documentation/fntguide.pdf#section.3) for the full details.