No. Parasnath (Parshvanath) and Shankar are not the same.

• Parasnath (Parshvanath) is the 23rd Tirthankara in Jainism. He is one of the spiritual teachers who attained omniscience and showed the path to liberation.
• Shankar (Shiva) is a major deity in Hinduism, not a Jain Tirthankara.

In both Digambar and Śvetāmbara traditions, Parshvanath is revered as a Tirthankara, but Shankar is not considered a Jain Tirthankara.