I think this does what you want in a reasonably robust way:
We can declare some new formats to colour the sortname and date:
\DeclareNameWrapperFormat{coloursortname}{\textcolor{red}{#1}}
\DeclareFieldFormat{colourparens}{\textcolor{blue}{\mkbibparens{#1}}}
\DeclareNameWrapperFormat needs at least version 3.12 of biblatex.
If you don't want the parentheses around the date coloured, just swap the order of \textcolour{blue} and \mkbibparens in the colourparens format.
Then we can redefine \fullcite to use these new formats. Normal citations and the bibliography are not affected.
\DeclareCiteCommand{\fullcite}
{\usebibmacro{prenote}}
{\usedriver
{\DeclareNameAlias{sortname}{default}%
\DeclareNameWrapperAlias{sortname}{coloursortname}%
\xpatchbibmacro{date+extradate}
{\printtext[parens]}
{\printtext[colourparens]}
{}
{}}
{\thefield{entrytype}}}
{\multicitedelim}
{\usebibmacro{postnote}}
I use xpatch to patch the date+extradate macro, since this macro changes depending on the value of the mergedate option passed to biblatex.
MWE
\documentclass{article}
\usepackage{xpatch}
\usepackage{xcolor}
\usepackage[style=authoryear,uniquelist=false,maxcitenames=2]{biblatex}
\addbibresource{biblatex-examples.bib}
\DeclareNameWrapperFormat{coloursortname}{\textcolor{red}{#1}}
\DeclareFieldFormat{colourparens}{\textcolor{blue}{\mkbibparens{#1}}}
\DeclareCiteCommand{\fullcite}
{\usebibmacro{prenote}}
{\usedriver
{\DeclareNameAlias{sortname}{default}%
\DeclareNameWrapperAlias{sortname}{coloursortname}%
\xpatchbibmacro{date+extradate}
{\printtext[parens]}
{\printtext[colourparens]}
{}
{}}
{\thefield{entrytype}}}
{\multicitedelim}
{\usebibmacro{postnote}}
\begin{document}
\verb|\autocite|: \autocite{baez/article}
\verb|\fullcite|: \fullcite{baez/article}
\printbibliography
\end{document}

biblatex, which uses a completely different way of formatting citations. – David Purton Sep 12 '19 at 15:12There is a general "annotations" feature for doing precisely such things if you are using biber
– PLK Sep 14 '19 at 14:48