Thorns of Bougainvillea and tendrils of Cucurbita are homologous organs. These are modified branches and are axillary in position. It means axillary branches in Bougainvillea are modified into thorns for protection from burrowing animals and in cucurbita into tendrils for climbing.
The analogous organs have almost similar appearance and perform the same function but these develop in totally different groups and are totally different in their basic structure and developmental origin. The phyllode of Ruscus or cladode of Asparagus are analogous to leaves of other plants.
The vestigial or rudimentary organs are useless remnants of structures or organs, which might have been large and functional in ancestors, eg, cutin covered stomata on the stem of cacti plants.