A client can ask a broker to buy “two IBM, one MSFT” either as a AA) custom basket or a BB) portfolio. The broker handles the two differently.
Only the Basket (not the portfolio) is “listed” on Bloomberg (but not on any exchanges). Client can see the pricing details in Bloomberg terminal, with a unique basket identifier.
Booking — the basket trade is recorded as a single indivisible position; whereas the portfolio trade gets booked as individual positions. Client can only sell the entire basket; whereas the portfolio client can sell individual component stocks.
Fees — There is only one brokerage fee for the basket, but 5 for a portfolio of 5 stocks.
The broker or investment advisor often has a “view” and advice on a given basket.
Corporate actions should be handled in the basket automatically.
I feel portfolio is more flexible, more informal than custom basket which is less formalized, less regulated than an index-tracking ETF.