Platform=Broker?

In tabloids, yes.

Traditionally in the world of investments you would buy stocks and shares through a stockbroker because you don't have a seat in the dealing room of the stock exchange to deal direct on the markets yourself. In the same way you would get insurance through an insurance broker rather than going direct to an underwriter (before people like "direct line" allowed you to buy insurance direct). So brokers, and in this case specifically, stockbrokers, have existed for decades.

Investment fund dealing platforms on the other hand have come more to the fore in the last few years. They are like a broker but originally for funds (unit trusts and open ended investment companies) rather than individual stocks; they offer their administration platform as a means for you to buy and hold your positions in funds. Historically they would be used by institutional investors and people using IFAs, while the general public would go through a pension company or insurance company or fund manager for whatever they wanted.

These days with the internet more people want to pick and choose their own investments and access them all in one place, so the big platforms have gone mainstream as "fund supermarkets".

By logical extension of the fact that people want to access things in one place, and ISA wrappers or SIPP wrappers legally allow you to hold funds and shares and bonds and all sorts in the one wrapper, many DIY investment platforms also have added stockbroking services so you can get shares and bonds and gilts and ETFs and investment trust companies that are listed on the market and priced every second. This is a different proposition from a firm that is a pure fund platform where they just book your orders to subscribe or redeem into or out of a fund which is priced once a day, and the fee structure is often different for the two parts of the business even if they do both.

For those platform firms who have added stock brokerage services to a core offering of investment fund access and administration, the sharedealing services are not always as feature-rich as those who have started out as brokers, and don't always cover as many global markets, but they get the job done. At the other end you have the traditional brokers who have added fund platform services, so they might have a comprehensively good broker product and use somebody else's platform in the background for funds with perhaps a more limited range than a true fund specialist.

And some platforms don't do stockbroking at all, while some brokers don't do funds at all.

But generally in the mainstream media the line between brokers and fund platforms and generalist investment platforms are a bit blurred so they call anyone who will sell you an investment and provide you a report, a "broker" or a "platform", interchangeably.