Bao uses the terms "soft" synthetics and "hard" synthetics to refer to two different types of synthetic assets, defined below.
Soft synthetics are tokens representing a basket of underlying tokens. Examples of well-known token baskets in the space currently are DPI, Indexed.Finance (CC10, ORA5, DEGEN, etc.) and PieDao.
Hard synthetics are synthetic tokens that link price to data. That data could itself be a price, like $TSLA stock price, the price of 1 ounce of gold, or something more exotic like the number of goals Neymar Jr scores, rainfall levels or crime rates, etc. The value of the synthetic asset is backed by collateral and can have various mechanisms to help it keep its peg. Common examples are being able to redeem the collateral at the rate the data says is correct, or by creating discounts to buy back and “repay” your synthetic position, or premiums on selling it, incentivizing more “borrowing”.