but when you buy a share, you are part of only the 8B thats being raised with the other 180 million shares, or do you have a small part of the whole 80~b valuation?

There are 80 billion dollars worth of shares that exist. However only 8 billion of those shares were released for the public markets. The remaining 72 billion dollars worth of shares are held outside of the public markets (insiders, vcs, the company itself, etc.)

Till such time those 72b shares do not become public, are these technically still referred to as options? Also, for ex-uber employees who still own shares, how does one restrict them to not sell those in the public market assuming they are part of the 72b or will they only be part of the 8b?

No, options are not the same as shares. Options are a contract that allows you to buy or sell shares at a certain price.

The employees are part of the 72 billion. All employees (current or ex) have a lock up period after the IPO where they are not allowed to sell.

thanks for your time and explanation!