How to place two tables vertically together in a double column layout paper

Question

I have two independent (not subfigs and related) tables that should appear aligned together vertically in a double-column layout format paper. I used one table wrapper and then minipage for each tabular (according to cannot use \caption under minipage and many other solutions), but the caption still appears for the last table. Here's the code:

\documentclass[11pt,a4paper]{article}
\usepackage{times}
\usepackage{latexsym}
\usepackage{amsmath}
\usepackage{algpseudocode}
\usepackage{graphicx}
\usepackage{multirow}
\usepackage{tabularx}
\usepackage{hhline}
\usepackage{arydshln}
\usepackage{url}
\usepackage{enumitem}
\usepackage{booktabs}
\usepackage{xcolor}
\usepackage{setspace}
\usepackage{hyperref}
\usepackage{titlesec}
\usepackage{capt-of}
\usepackage{varwidth}
\usepackage{wrapfig}
\usepackage{ctable}
\usepackage{adjustbox}
\usepackage{float}
\restylefloat{table}
\usepackage{subfiles}
\usepackage{amssymb}
\usepackage{enumitem}
\usepackage{colortbl}
\usepackage{multirow}
\usepackage{array}
\usepackage{cleveref}
\usepackage{titlesec}
\usepackage{subfig}
\usepackage{lipsum}
\begin{document}
\begin{table*}[!htb]
\begin{minipage}{.55\textwidth}
    \centering
    \small
\def\arraystretch{1.0}\tabcolsep=3pt    
\begin{tabular}{lcccccccc}
  \toprule
    & \multicolumn{2}{c}{\textbf{AAA1}} & \multicolumn{2}{c}{\textbf{AAA2}} & \multicolumn{2}{c}{\textbf{AAA3}} &  \multicolumn{2}{c}{\textbf{AAA4}}\\
    A1                     & A2              & A3  & A4              &A5           & A6           & A7      & A8 & A9 \\ \toprule
       \textsc{BLAAAAA}  &     -   & - &            -      &       -      &        -     &    - & -  &  - \\ 
       \textsc{BLAAAAA}  &     -   & - &            -      &       -      &        -     &    - & -  &  - \\ 

       \textsc{BLAAAAA}  &     -   & - &            -      &       -      &        -     &    - & -  &  - \\ 
      \midrule
       \textsc{BLAAAAA}  &     -   & - &            -      &       -      &        -     &    - & -  &  - \\ 
       \textsc{BLAAAAA}  &     -   & - &            -      &       -      &        -     &    - & -  &  - \\ 
       \textsc{BLAAAAA}  &     -   & - &            -      &       -      &        -     &    - & -  &  - \\ 
       \textsc{BLAAAAA}  &     -   & - &            -      &       -      &        -     &    - & -  &  - \\ 
       \textsc{BLAAAAA}  &     -   & - &            -      &       -      &        -     &    - & -  &  - \\ 
    \bottomrule
\end{tabular} 
\caption{Capt1}
\label{tab:1}

\end{minipage}
\begin{minipage}{.45\textwidth}
% \subfloat[First caption]{
    \centering
    \small
    \def\arraystretch{1.0}\tabcolsep=3pt

    \begin{tabular}{@{}lrrr@{}}
        \toprule
        A1            & A2 & A3 & A4 \ \midrule
        BLAAAAA     & -   & -    & -     \
        BLAAAAA     & -   & -    & -     \
        BLAAAAA     & -   & -    & -     \
        BLAAAAA     & -   & -    & -     \
        BLAAAAA     & -   & -    & -     \
        BLAAAAA     & -   & -    & -     \
        \bottomrule
    \end{tabular}
    % \end{table}
    \caption{Capt2.} 
    \label{tab:2}
\end{minipage} 
\end{table*}
\end{document}

and the results (only capt2 should be there):

How can I see the captions of the two tables, and also align them visually? Here's what I want:

Answer 1

Edit: The first proposed solution is now adapted to the new information added to your question:

Above result are produced with your code (first example) and by use of the tabularx package (second example). Both gives expected result, so it is not clear what is your problem. For further help please provide an MWE which reproduce your problem.

\documentclass[11pt,a4paper, twocolumn]{article}
\usepackage{booktabs, tabularx}
\newcolumntype{C}{>{\centering\arraybackslash}X}
\usepackage{lipsum }
\begin{document}
% your code with use of dummy tables
\begin{table*}
\begin{minipage}[b]{.55\textwidth}
    \centering
\begin{tabular}{ccc}
\toprule
text    &   text    &   text    \
\midrule
text text text    & text text text & text text text   \
text text text    & text text text & text text text   \
\bottomrule
\end{tabular}
    \caption{capt 1}
    \label{tab1}
\end{minipage}%
\begin{minipage}[b]{.45\textwidth}
    \centering
\begin{tabular}{cc}
\toprule
text    &   text    \
\midrule
text text text & text text text   \
\bottomrule

\end{tabular}
    \caption{capt 2}
    \label{tab2}
\end{minipage}
% solution with `tabularx and use the same dummy tables as before
\vspace{3\baselineskip}
    \begin{tabularx}{\linewidth}{>{\hsize=1.1\hsize}C
                                 >{\hsize=0.9\hsize}C}
\begin{tabular}[b]{ccc}
\toprule
text    &   text    &   text    \
\midrule
text text text    & text text text & text text text   \
text text text & text text text   \
\bottomrule
\end{tabular}   &   \begin{tabular}[b]{cc}
                    \toprule
                    text    &   text    \
                    \midrule
                    text text text & text text text   \
                    \bottomrule
                    \end{tabular}   \[-3ex]
\caption{First table}
                &   \caption{Second table}
    \end{tabularx}
\end{table*}
\end{document}

Answer 2

Table captions are usually put on top of tables whereas figure captions are put below the graphics. What do you think of this (having had to invent what your code might look like)?

% tablesprob.tex  SE 579912
\documentclass[twocolumn]{article}
\usepackage{lipsum}
\begin{document}
\begin{table}%[!htb]
\begin{minipage}{.55\textwidth}
    \centering
    \small
    \caption{capt1}
    \begin{tabular}{|c|} \hline
    An entry \ \hline
    \end{tabular}
%    \caption{capt1}
    \label{tab1}

\end{minipage}
\begin{minipage}{.45\textwidth}
    \centering
    \small

    \caption{capt2}
    \begin{tabular}{|l|r|} \hline
    left & right \ % \hline
    LEFT & RIGHT \ \hline
    \end{tabular}
%    \caption{capt2}
    \label{tab2}

\end{minipage}
\end{table}
Two tables, \ref{tab1} and \ref{tab2}.
\lipsum[1-10]
\end{document}