Screen printing is the process of printing your logo or design onto the fabric using special ink. Screen printing designs onto fabric is an automated process completed one colour at a time using mesh to transfer into on the fabric, which is then dried to set the print or cure it.
Contrarily, machine embroidery is an automated process using a sewing machine or computerised embroidery machine that creates patterns on textiles using a needle and thread. Most commonly embroidery machines have 12 or more sewing heads with up to 15 needles per head (12 items can be found embroidered simultaneously and the logo can use to up 15 thread colours.
You can read more about the differences between the two options here.