As a teacher and native speaker, I would say that the answer is: 'not much'. It seems more down to idiolect than a meaningful semantic difference.

Toward or towards means in the direction of somewhere "he headed off toward(s) the high street" are the same but towards is more common. They are therefore the same in this context PLEASE NOTE in other contexts TOWARDS and never toward means against something "he felt a real loathing towards her" you cannot use toward for this type of sentence. It can be a little bit of an advanced subject but I am not going to go into that. Italki is a learners platform and not an academic scholarly platform. I'm sure you will receive answers that debate it, if you are interested then you can come back and check out later comments.

In the U.S., "towards" is NOT a word and should never be used. You should always use "toward." Now, many Americans will use the word "towards" in their speaking, but that doesn't make it correct.