The style of these two settings is defined by the CursorLine and CursorColumn highlight groups.
If I query these two on my Vim, I get:
CursorColumn xxx term=reverse ctermbg=242 guibg=Grey40
CursorLine xxx term=underline cterm=underline
So what we want to do is make CursorLine look more like CursorColumn.
For terminal Vim, with colors, we're most interested in the
cterm group of settings (
term=reverse is for B&W terminal, the
gui ones are primarily for gvim.)
So one simple way is:
hi CursorLine cterm=NONE ctermbg=242
Another way forward is to "link" these styles so they look the same:
hi clear CursorLine
hi link CursorLine CursorColumn
If you also enable line numbers, you might want to look at this group:
CursorLineNr xxx term=bold cterm=underline ctermfg=11
That's the highlighting for the line numbers on the current line. You might want to have them match the background you're using for the rest of the line and disable the underlines there as well.
These might be controlled by your
colorscheme, so if you set them in your vimrc you might want to do so after you set a colorscheme.
That might still not be enough if you tend to switch colorschemes or switch background from dark to light or vice-versa. To have these always apply after a colorscheme, you can also create an autocmd that sets them up after a colorscheme is loaded.
au ColorScheme * hi clear CursorLine
\ | hi link CursorLine CursorColumn
You can also add any commands you decide to use for CursorLineNr to this group as well.