These two words are used interchangeably and have the same meaning. Both versions are correct. “Toward" is more common in the United States, while “towards" is more common in British English. If you're looking for a convention to follow when debating whether to add the “s," that's as stringent as it will get.
This isn't true for all words that sound the same. “All ready" and “already" have two distinctly different meanings. “All ready" signifies preparedness, while “already" is an adverb that means “by a certain time" or “previously." Even words distinguished only by an added “s" can have different meanings. For example, “beside" is a preposition meaning “next to" or “alongside:"
In the winter, she sat beside the radiator to stay warm.
“Besides" is also a preposition and it means “in addition to" or “other than:"
Besides his wedding ring, Joe didn't take anything of value with him.
Don't apply any one rule to what seem to be similar word pairs. Each may have its own unique rule. Look them up until they stick in your memory.