I can see there’s a bit of confusion here about comparing mid, bid and intraday exchange rates!
So here’s a quick recap of FX market infrastructure basics, and a comparison of MasterCard/travel shop/ATM exchange rates! 
What’s the price for a Currency?
In a stock or commodities market, contracts are priced in monetary terms, usually the local currency or USD. For example, the current price of an $AAPL share is around $115, and a barrel of oil is $40.
But FX is money itself, so we have to express the price as the rate of exchange for one unit of currency (the Quote currency) for one unit of the other currency (the Base currency). For example:
- EUR/GBP: I have euros and want to buy pounds
- GBP/EUR: I have pounds and want to sell them for euros
Exchange Rates
The exchange rate is quoted to several decimal places - usually 4 DP, depending on the currency pair. For example, 1.3914.
Why do we need so many decimal places? It’s not possible to have £0.0001 or €0.0001 in your bank account. But contract sizes in the wholesale FX market can be huge - easily tens or hundreds of millions. At this level, the granularity provided from additional precision allows market pricing to be much more efficient (competitive).
Spot Market
The wholesale market used by banks, governments, investment funds and corporates to buy and sell foreign currency is called the Spot Market. Spot means “on the spot” prices for soonest delivery possible. The standard settlement period for spot trades is two business days.
Around $5 trillion per day is traded on the spot market. It is by far the biggest and most liquid market in the world.
Exchanges
Contracts are traded either over-the-counter by banks, or on exchanges like FXAll, Hotspot, EBS and Currenex. All exchanges use a continuous auction style called a Limit Order Book. The software at the heart of an exchange that manages the Order Book is called a Matching Engine, and must be very fast and reliable.
Normally, trading firms pay a lot of money to see the exchange’s order book contents (called Level 2 Market Data), because the additional information gives them a trading advantage. But luckily for us, Bitcoin exchanges work in exactly the same way, and publish real-time data for free, so we can use that as an example. Here is Coinbase’s live order book:
The order book is divided into two halves. On the left are the Bids (buyers), and on the right are the Asks (sellers). Each side shows the total Liquidity (amount available to buy or sell) at each Price level.
The outward-curving shape of the order book demonstrates basic supply and demand. Buyers (on the left) want to secure the lowest price possible, so there are more buyers at the outside of the book (where prices are lower), than in the centre. Similarly, sellers (on the right) only want to sell for the highest price possible, so they crowd towards the right hand side (where prices are highest). If an order crosses over, then a trade is executed, and the orders that were filled are removed from the book.
The order at the top of the bid (left) side is called the Best Bid, and represents the highest (most attractive) price you can currently sell for. On the ask (right side), the Best Ask is the order with the lowest (most attractive) price you can buy for.
Bid/Ask Spread
The gap in the middle is called the Bid-Ask Spread. In stressed market conditions (e.g. a crash), the spread widens as the risk of loss increases and participants withdraw their liquidity.
The Spread is measured in units called Pips. For example, a change from 1.3914 to 1.3915 is a 1 pip increase.
(Side note: In interest rate and credit markets, the equivalent of Pips are called Basis Points.)
Crosses
Not every currency pair can be traded. For example, as far as I am aware there is no exchange in the world you can trade ILS/NZD directly, because the market is too small (illiquid). Currency pairs like these are ‘crossed’ through another currency e.g. ILS/USD → USD/NZD. Typically, most currencies can only be traded against EUR, JPY, GBP and CHF, and any direct rates you see are indicative through triangulation.
Official Daily Rates
Exchanges can process many thousands of orders per second, constantly fluctuating the price. So how do we publish a single, official exchange rate for a given day?
We could take the average rate from all trades throughout the whole day, but if a lot of very small trades (say £1 each) and one large trade (£1 billion) were executed, then it wouldn’t be a true representation of the volume traded - it would be skewed towards the small trades. Also, should the measurement be equally weighted throughout the day, or are most people only interested in the end result?
In reality, the most commonly-used official daily exchange rates rates are Fixed based on a 60 second sample at a given time of day:
The WM/Reuters benchmark rates are determined over a one-minute fix period, from 30 seconds before to 30 seconds after the time of the fix, which is generally 4 pm in London. During this one-minute window, bid and offer rates from the order matching system and actual trades executed are captured. Since trades occur in milliseconds, only a sample is captured, rather than every trade. The median bid and offer are calculated using valid rates over the fix period, and the mid-rate is then calculated from them.
Mid Rates
The most common exchange rate you see in news articles and on TV is the Mid Rate, calculated as the average of the Best Bid and Best Ask price.
The Mid Rate can be useful for historical analysis, but it is important not to use it for comparing prices:
- It hides the fact that there are different prices for buying and selling (supply and demand)
- It is a purely Indicative rate - it is never possible to buy or sell the mid rate because there is no liquidity (orders available) at that price
(Side note: TransferWise uses the Mid Rate but this is unique to TransferWise - they appear to be running a different style of auction with fixed daily rates instead of a true limit order book).
Comparing Spreads
Dealers make money by adding either a Commission (percentage of the total amount), a flat Fee (e.g. £2), or their own Margin to the spread, reflected in the advertised exchange rate. Margin is the most common, and is usually advertised as “commission free”, however the spread can be very wide!
I did some analysis and compared EUR/GBP spreads between various retail FX brokerages, travel money shops and the MasterCard base rates:
- Wholesale: < 1 pip
- Retail FX brokerage account: 1 to 5 pips
- Thomas Exchange: 150 pips
- ATM in Europe using local currency: 500 pips
- ATM in Europe using “convert to home currency”: 700 pips (never do this!)
- Airport foreign exchange shop: 900 pips!
The MasterCard rates are incredibly good. As @aspark noted, if you need to buy €1,000 of travel money, you could save between £10-90 compared to a travel money shop or ATM. 