I asked the Internet, and this is what some random person thinks:
"Both ‘Spectra’ and ‘Dyneema’ are HDPE (High Density Polyethylene) fibres. However, Dyneema (Manufactured in Europe and Asia by Toyobo/Dyneema, DMS), is recognized as being of a slightly ‘lower quality’ than the American version "Spectra". (The quality of Dyneema generally is very good). Also, the individual filaments that make up a Dyneema yarn are smaller than individual fibres in a spectra yarn; this translates to better abrasion resistance."
I should warn you that the Internet has been wrong before.