For a unicast packet, an ARP request must be sent to resolve an unknown layer 2 address. Depending on how the route is configured (static or dynamic), the router will either ARP for the the next hop address or the the layer 3 address in the packet. Either way, the forwarding router will be sent the MAC of the next hop router.
The packet is forwarded as part of the routing process. What is switched at layer 2 is the source/destination MAC, something that does not happen with traditional switching. the layer 3 information will remain unchanged.