Can I show different tabs to different customers or products?

Yes. A tab is attached to products through entity selector rules (individual products, categories, manufacturers or suppliers), and you can narrow it further by customer group, a start/end schedule, visitor country and stock status (show only when the product is in stock or only when it is out of stock). A tab with empty targeting is treated as applying to all products, so you can mix broad tabs with tightly targeted ones. The rules are evaluated on each product page, so the same tab record can appear on many products without being copied.