\documentclass{article}

\usepackage{float}
\usepackage{tikz,caption}
\usepackage{ifthen}

\begin{document}

\newcommand{\titlename}[1]
{%
    \ifthenelse{\equal{#1}{a}}{First}{}%
    \ifthenelse{\equal{#1}{b}}{Second}{}%
}

\foreach \y in {a,b}{
  \foreach \a in {No,Yes}{
    \begin{table}[H]
    \captionsetup{width=.9\linewidth}%
    \caption{\protect\titlename{\y}, \a  ~Other Text}
    \end{table}
  }
}

\end{document}