Within Shopventory, the main difference is that a barcode can be re-used with multiple variants, while SKUs must be unique.
If you need to, you can generate a SKU number for any Variant that doesn't already have one right in the SKU field in the Edit Product panel.
Each POS handles these a little differently.
Shopify*: supports SKU and barcode
Clover**: supports SKU and barcode
Square: supports SKU only
PayPal Here: supports barcode only
WooCommerce: supports SKU only
*Only the SKU can scanned at the Shopify POS.
**Our barcode will map to the "Product Code" in Clover.
Even if your provider doesn't support a field, you can still use it internally in Shopventory. Both SKUs and Barcodes are optional.