[Tex/LaTex] why does \mathbf{\rho} do not show as bold, but \boldsymbol{\rho} do

Question

May be related How can I get bold math symbols?

I use Scientific word, and when I wanted to make some symbols and letters as vectors. So I select, in math mode, a symbol, and then using the menu, select the bold option, it generates this code, using \mathbf. Here is an example

\[
\mathbf{V}_{p/2}=\mathbf{\dot{R}}_{3/2}+\mathbf{\omega}_{3/2}\times
\mathbf{\rho}_{3p}+\mathbf{\dot{\rho}}_{3p,r}%
\]

The above, when compiled with Latex, shows the \rho as not bold. Screen shot below.
Next, I changed the selection from the menu to boldsymbol instead of bold and this the new code generated:

\[
\mathbf{V}_{p/2}=\mathbf{\dot{R}}_{3/2}+\mathbf{\omega}_{3/2}\times
\boldsymbol{\rho}_{3p}+\boldsymbol{\dot{\rho}}_{3p,r}%
\]

Now the \rho does show as bold when compiled. I was wondering why that is. I would have thought both will be bold, but different fonts? Bit confusing, since I thought what shows on the screen will be what shows in the PDF file. (ps. this issue affects \omega as well as \rho but not the letter R as can be seen)

Here is a screen shot. I am using TL 2013 to compiled the .tex code. (I only use SW to type in the Latex via the GUI). Compiled on Linux mint.

Fyi, the options I have to change the fonts are these shown in this screen shot.

Answer 1

Most math symbols (in classic TeX) come from fixed fonts (one of 16 font families assigned to the math formula). Some characters (but typically just upper and lower case latin letters and digits) can be assigned a variable family in which case they pick up the current math group (\fam primitive).

\boldsymbol is more or less \mbox{\boldmath$#1$}} so makes a nested math expression in which the entire font assignment is changed.

\bm is typically more efficient and gives better spacing as (if there is a slot available) it uses a free slot in the existing version.

unicode-math package for xetex/luatex changes things.