This is an early strike of the William H. Taft with an early version of the reverse die. The most noticeable difference is that the reverse of this medal has George Morgan's signature near the rim at 5 o'clock. Later strikes, struck into the late 20th century do not have his signature. In fact, in "Medals of the United States Mint" by Kenneth Failor and Eleanora Hayden, the medal is solely attributed to Charles E. Barber. You will also notice some differences in the style and placement of the lettering on the obverse.

For comparison, I have included a photo that includes a medal struck earlier and a medal struck later than the one for sale. You will note even more differences than I have described above.

Most collectors haven't noticed the differences and an advanced collection would include all varieties, especially the earliest die variety. There may be more varieties as well. 

The earliest and latest medals pictured are for comparison only. They are not included in the sale of this medal.