Historically, at least in France post Napoléon and until ww2, the center was the current government, the right wanted to go back to a previous system/societal organisation (at first monarchism, privilege and landed nobility (to some degree, see Montesquieu), then to a parliamentary monarchy, then to 18th century capitalism... Etc) while the left wanted change never tested before (first parliamentary monarchy, then a republic, then allowing women to vote... Etc).
The fact that left and right became more indiscernible might be because nowadays, most politicians wants untested changes in some domains, staying the course in others, and going back to a previous state in a few.
So definition like 'the right wants more freedom, the left more equality' to me misses the point. The real interest of left and right is to discern what your endgoal society is. If you want to get back to guilds and corporatism, you are economically far right. If your policies help get back to the robber barons state by allowing monopolies and stop regulations on natural monopolies, you are right wing, idc if you are a democrat or a republican.
Sometimes, it is just balancing the two.