The main differences between most neutral density(ND) filters and a solar filter(white light) come down to the filtering strength and the filtering properties. The strength of the more common ND filters range from 1-10 stops, where as for safe solar eclipse viewing you want to use 13 or more stops for imaging and 16 or more stops for direct viewing. More information of that topic can be found here (Can I photograph a solar eclipse using a 10-stop Big Stopper (+ extra ND?))
As for the filtering property differences, standard ND filters typically only cover the visible spectrum where as solar filters will also cover Infra-red(IR) and Ultraviolet(UV) radiation. I'm not aware of a regular ND filter that includes IR/UV attenuating and is 13+ stops, so I would be wary of both your camera sensor and eyes using any ND filter setup.
Less Critical Differences
Some solar filters actually render the sun in different colors such as yellow, orange, blue, and white - something you won't see in a standard ND filter.
You can read anecdotes all over the internet about people who do capture eclipses without proper solar filters, but ultimately it is not recommended if you want to protect yourself and your equipment.
There are many ways to measure the transmissiveness of filters. Be very careful comparing ND scales to optical density (OD) scales for solar filters (i.e. ND 8192 = OD 3.9 and ND3 is nowhere near OD3!), and when in question, don't ever bet your eyes on something you aren't sure of!