What is the difference between Je vous aime and Je t'aime ?Feel free to just provide example sentences.

Je vous aime is the formal version of je t'aime. It shows higher respect to the person you're talking to, for example if you don't know the person very well. Or it can be used if you're talking to several people.
for example:
a mother talking to her child would say "je t'aime", and a mother talking to her children would say "je vous aime".
If I'm talking to my boyfriend I would say "je t'aime", but if I'm talking to a complete stranger I would say "je vous aime". (well I don't really know if there is a situation when I would say that to a stranger but anyway...)