They aren't exactly the same, and I'll give you an example to show you how. When I say "On the way to the store, I saw a cat," I could have seen the cat anywhere I was while I traveled to the store-- I could have seen it on the bus that took me there, on the street I was walking on, etc. But when I say "On the way INTO the store, I saw a cat," I am more specifically referring to while I was walking inside or arriving at the store, so in this sentence, the cat had to be either right outside or right inside the store. I hope this helps!