As Poolshark stated, because the primary panel in the shop is a SUBPANEL feed from the main panel at your house, grounds and neutrals must be separated and because it is a separate structure, it must also have 2x ground rods buried at least 6ft apart and connected via solid copper grounding electrode conductor sized per NEC 250.66. The bonding screw in your current subpanel at the shop does not appear to be installed, as it would be installed in the hole to the left of your neutral lug at the top of the panel bussing.
When you install your second subpanel in your shop, to be fed from the current 100A panel, this must be wired in a similar fashion but does not require ground rods, as the building will be grounded by means of the main 100A panel and its grounding electrode conductor / ground rods.
Your second subpanel shall have 2x line/ungrounded conductors, a neutral/grounded conductor, sized according to NEC 310.16 per the size of disconnect breaker that you place in the 100A shop subpanel and a grounding conductor sized per NEC 250.122 and the grounds and neutrals must be separate in this panel as well.