Set option autoneside=false
for package scrlayer-scrpage
if you want to use both chapter and section titles in a onesided document.
Set class option headings=optiontohead
if the optional argument of sectioning commands should be used for the page header and not for ToC by default.
Example:
\documentclass[
headings=optiontohead,
twoside=false
]{scrbook}
\usepackage[autooneside=false,automark]{scrlayer-scrpage}
\clearpairofpagestyles
\ihead{\leftmark}
\ohead{\rightmark}
\cfoot*{\pagemark}
\usepackage{lipsum}% only for dummy text
\begin{document}
\tableofcontents
\chapter[Short chapter title]{Long chapter title for document and TOC}
\section[Short section title]{Long section title for document and TOC}
\lipsum
\chapter{A chapter}
\section{A section}
\lipsum
\end{document}


Update (regarding a comment below)
To avoid two equal entries on both sides of the header (eg. in a TOC with more than one page or a chapter without sections) you can use
\ohead{\ifstr{\leftmark}{\rightmark}{}{\rightmark}}
Example:
\documentclass[
headings=optiontohead,
twoside=false
]{scrbook}
\usepackage[autooneside=false,automark]{scrlayer-scrpage}
\clearpairofpagestyles
\ihead{\leftmark}
\ohead{\ifstr{\leftmark}{\rightmark}{}{\rightmark}}
\cfoot*{\pagemark}
\usepackage{lipsum}% only for dummy text
\begin{document}
\tableofcontents
\chapter[Short chapter title]{Long chapter title for document and TOC}
\lipsum[1-12]
\section[Short section title]{Long section title for document and TOC}
\lipsum
\chapter{A chapter}
\section{A section}
\lipsum
\end{document}
