For the most part people seem to use these terms (along with several others) to refer to "a relatively low cost (in terms of time and resources) test conducted to determine of a particular release or build is adequate for further testing." These tests may be manual or automated. I'm sure that there are folks that would make a distinction between the two, but I'm also certain that there is no general consensus over what that distinction would be.
If you're interested, the term "smoke test" comes from plugging in an electronic device after it has been shipped to a distribution point but before delivery to the final customer. If the device smoked when it was plugged in, the distribution point would send that device back to the shipper and request a replacement instead of sending it on to the final customer.