What are the differences and similarities among Paymium, Bitpay, Coinbase, etc.? Google news in recent months has turned up a story about a company in France called Paymium that has been licensed as a bank (without going into just what the company does), and another company that has moved to Atlanta, called Bitpay, which enables customers who have web sites to accept bitcoin payments.  The headlines about the latter seemed to be about the fact that they'd raised something over a half-million dollars from a small number of investors.  Google news didn't include anything about Coinbase, as far as I recall.  But a glance at websites makes it look as if they might all be in approximately the same business.

Can someone compare and contrast these companies, including, but not limited to, differences and similarities in what they do?  And are there other such companies that are notable and that I've missed here?
Paymium, operates Bitcoin-Central.net market exchange.  That exchange has partnered with a financial organization such that your EUR balance held at the exchange will be (once they go live with that) guaranteed by the government.  They will only be doing BTC/EUR when this goes live.  Currently they offer BTC/USD, BTC/GBP and BTC/EUR markets but no fiat balances are currently guaranteed.

BitPay is a payment processor for E-Commerce as well as for bricks and mortar / point-of-sale.  This allows a business to accept bitcoins for payment and the proceeds are delivered to the merchant as directed.  This could be 100% fiat (e.g., all bitcoin sales get converted to USDs immediately, or a mix, .. like 30% USD, 70% BTCs, etc.)   The currently can send payments to merchants in U.S., Mexico, Canada and several nations in Europe.

Coinbase account holders get a secure web-based bitcoin wallet, and by linking a U.S. bank account, the ability to buy/sell bitcoins directly from/to Coinbase at a USD conversion rate that is very close to the last price quoted from London based bitcoin exchange Bitstamp. Coinbase itself is not a crypto-currency exchange. Coinbase also offers bitcoin transaction processing services to merchants.

There are quite a few exchanges.  The bitcoin.it Wiki has Buying bitcoins and Selling bitcoins indexes that are fairly comprehensive as to the options available.