[fernandopj]

The basic difference:

In an IPO the company puts private shares in the open market and gets money from it, priced at the IPO price. Whoever has (private) shares now has public shares and can trade whenever they want.

In a Direct Listing the company often already traded shares "openly" but not in a "public" way, but now wants it listed publicly so retail investors can trade it, and there's no immediate need of capital so the objective isn't to get a funding from offering shares in an IPO.