THE DIFFERENCE is that spermatophyte is (botany) any plant that bears seeds rather than spores while pteridophyte is any plant of the division pteridophyta, of simple vascular plants that reproduce via spores rather than seeds and that alternate generations of diploid (sporophyte) and haploid (gametophyte or prothallus) forms
The main difference between these two classes is that: Pteridophytes are vascular plants but they do not produce flowers and seeds which mean their source of reproduction is unknown or hidden. Examples are ferns, horsetails and lycophytes. On the contrary, Spermatophytes as the name indicates, are seed bearing plants.
