Please explain the main differences (use cases) between Targeted LDP and Directed LDP in MPLS ?
Directed LDP is not a term that appears in the LDP specification (RFC 5036.)
Perhaps you're trying to understand the difference between Basic Discovery which uses LDP Link Hellos and Extended Discovery which uses Targeted Hellos. Targeted LDP is for exchanging messages with a distant, non-adjacent peer.
Targeted LDP can allow routers to use LDP-signaled LSPs to reach next-hops connected to each-other by sending traffic through the data-plane with an additional, inner label which is signaled using tLDP. In today's networks, BGP, with its different scaling properties, has taken over much of the role for which tLDP can be used.