Vintage style is usually a classic design that is accessorized in such a way that it hints at a specific period of fashion from a bygone era.
One could make an argument that all vintage style is classic as well, but not all classic style is retro. I would also like to point out that even though by definition a classic style is not trendy, every now and again something that is considered classic becomes uber trendy. For example, a few years ago trench coats were all the rage and you could find them everywhere. Now they have settled into the background and are once again considered a classic. There are other trends that one might assume is a classic style when in fact it is just a design aspect that has been seen in the past and has once again become a trend, and when that trend is played out it won’t be seen again for years. I point to the peplum as an example. It was a trend in the ’40s, ’80s and right now. I bet you next fall we won’t be seeing them at all because that trend is coming to an end.