Instead of answering the broad question of how math fonts vary from text fonts across document classes, here's a way you can see which fonts are used.
\showoutput inserts the page construction details in your .log, including the choice of fonts. The minimal example
\documentclass{article}
\showoutput% Show output page construction
\begin{document}
-1
$-1$
\end{document}
shows in the .log the choice of encoding and fonts:
....\OT1/cmr/m/n/10 -
....\OT1/cmr/m/n/10 1
....
....\mathon
....\OMS/cmsy/m/n/10 ^^@
....\OT1/cmr/m/n/10 1
....\mathoff
The font used for 1 and $1$ are the same, but not for - and $-$. Similarly, the following minimal example (loading a different font via cfr-lm)
\documentclass{article}
\showoutput% Show output page construction
\usepackage{cfr-lm}
\begin{document}
-1
$-1$
\end{document}
shows in the .log the choice of encoding and fonts:
....\T1/clm2j/m/n/10 -
....\T1/clm2j/m/n/10 1
....
....\mathon
....\OMS/lmsy/m/n/10 ^^@
....\OT1/lmr/m/n/10 1
....\mathoff
$-1$which is not same as-1. This is a duplicate, i'll see if I can find.... – David Carlisle Aug 17 '16 at 09:21