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Just say Bitcoin. Bitcoin Classic is part of bitcoin cash. Anyway the LN can do million to billion tps.
For on chain scaling bitcoin, bitcoin can do 39 tps with about less than 3mb blocks. https://steemit.com/bitcoin/@sames/segwit-bech32-batching-others-will-lead-to-bitcoin-reaching-passing-ethereum-on-chain-tps-level
Bitcoin does plan on increasing block size just when segwit has reached its limit.

How can Bitcoin Cash be part of Bitcoin Classic if the BTC original Bitcoin is older than Bitcoin Cash?

Bitcoin classic is an alt node that supports bitcoin cash as their real bitcoin: https://bitcoinclassic.com/news/closing.html