Using the cmbright package in a limited range of my document

In PDFLaTeX,

documentclass{article}
usepackage[T1]{fontenc}
usepackage{cmbright}
usepackage[paperwidth=10cm]{geometry}

renewcommandfamilydefault{rmdefault}

begin{document}
Text in Computer Modern Roman,
textsf{and Computer Modern Bright.}
end{document}

To change only the sans-serif text font, and not the default font or the math fonts:

documentclass{article}
usepackage[T1]{fontenc}
renewcommand{sfdefault}{cmbr}

begin{document}
Text in Computer Modern Roman,
textsf{and Computer Modern Bright.}
end{document}

Then add sffamily to every type of text you want to appear in sans-serif, such as captions.

If you wanted to use CM Bright Greek letters in math mode, the simplest way to do that is probably to load it as the OML sans-serif math alphabet through isomath.

You could also do something like (untested):

DeclareSymbolFont        {sans} {OML}{cmbrm}{m}{it}
SetSymbolFont      {sans}{bold} {OML}{cmbrm}{b}{it}

DeclareMathSymbol{alpha}{mathalpha}{sans}{11}
DeclareMathSymbol{beta}{mathalpha}{sans}{12}
DeclareMathSymbol{gamma}{mathalpha}{sans}{13}
DeclareMathSymbol{delta}{mathalpha}{sans}{14}
DeclareMathSymbol{epsilon}{mathalpha}{sans}{15}
DeclareMathSymbol{zeta}{mathalpha}{sans}{16}
DeclareMathSymbol{eta}{mathalpha}{sans}{17}
DeclareMathSymbol{theta}{mathalpha}{sans}{18}
DeclareMathSymbol{iota}{mathalpha}{sans}{19}
DeclareMathSymbol{kappa}{mathalpha}{sans}{20}
DeclareMathSymbol{lambda}{mathalpha}{sans}{21}
DeclareMathSymbol{mu}{mathalpha}{sans}{22}
DeclareMathSymbol{nu}{mathalpha}{sans}{23}
DeclareMathSymbol{xi}{mathalpha}{sans}{24}
DeclareMathSymbol{pi}{mathalpha}{sans}{25}
DeclareMathSymbol{rho}{mathalpha}{sans}{26}
DeclareMathSymbol{sigma}{mathalpha}{sans}{27}
DeclareMathSymbol{tau}{mathalpha}{sans}{28}
DeclareMathSymbol{upsilon}{mathalpha}{sans}{29}
DeclareMathSymbol{phi}{mathalpha}{sans}{30}
DeclareMathSymbol{chi}{mathalpha}{sans}{31}
DeclareMathSymbol{psi}{mathalpha}{sans}{32}
DeclareMathSymbol{omega}{mathalpha}{sans}{33}
DeclareMathSymbol{varepsilon}{mathalpha}{sans}{34}
DeclareMathSymbol{vartheta}{mathalpha}{sans}{35}
DeclareMathSymbol{varpi}{mathalpha}{sans}{36}
DeclareMathSymbol{varrho}{mathalpha}{sans}{37}
DeclareMathSymbol{varsigma}{mathalpha}{sans}{38}
DeclareMathSymbol{varphi}{mathalpha}{sans}{39}
DeclareMathSymbol{Gamma}{mathalpha}{sans}{0}
DeclareMathSymbol{Delta}{mathalpha}{sans}{1}
DeclareMathSymbol{Theta}{mathalpha}{sans}{2}
DeclareMathSymbol{Lambda}{mathalpha}{sans}{3}
DeclareMathSymbol{Xi}{mathalpha}{sans}{4}
DeclareMathSymbol{Pi}{mathalpha}{sans}{5}
DeclareMathSymbol{Sigma}{mathalpha}{sans}{6}
DeclareMathSymbol{Upsilon}{mathalpha}{sans}{7}
DeclareMathSymbol{Phi}{mathalpha}{sans}{8}
DeclareMathSymbol{Psi}{mathalpha}{sans}{9}
DeclareMathSymbol{Omega}{mathalpha}{sans}{10}

In LuaTeX or XeTeX:

documentclass{article}
usepackage{unicode-math}
usepackage[paperwidth=10cm]{geometry}

setsansfont{CMU Bright}[Scale=MatchLowercase]

begin{document}
Text in Computer Modern Roman,
textsf{and Computer Modern Bright.}
end{document}

To load only its Greek letters in math mode, you would do something like:

setmathfont{Latin Modern Math}
setmathfont{CMU Bright}[range=up/{Greek,greek}]
setmathfont{CMU Bright Italic}[range=it/{Greek,greek}]