There is a good deal of confusion over these two products and this was deliberately, IMHO, created by Sky. The Beeb and Sky have an uneasy relationship. Over many years Sky has created itself a virtual monopoly of satellite broadcasting in the UK. Say satellite TV to anybody and they'll automatically think of Sky and nothing else. For many years, the Beeb paid Sky many millions each year to carry all their channels. A few years ago, their agreement came up for renewal and the Beeb managed to come up with a better idea. They rented space on the Astra satellite (same as Sky) directly from SES-Astra then just paid Sky to include their channels in Sky's EPG. This still costs the Beeb many millions a year so recently, when ITV's contract with Sky expired, the Beeb managed to encourage them to switch to their own service - called Freesat. Sky found out what was going on and, presumably before the Beeb has registered it as a trademark, started using the name 'Freesat from Sky' to offer a similar service but still retain control of the EPG.
There are many thousands of free-to-air satellite channels available in the UK from several satellites. You can buy a simple FTA receiver to view them (look for Lidl's occasional satellite kit offer for about £70) but these have a very limited EPG. You can usually see the name of the current program, possibly get a short description and, if you are very, very lucky, get the name of the following programme. Also, these channels have to be configured by hand so, as channels frequently come and go, it all becomes a lot of hard work.
Freesat is all about wrestling control of the EPG back from Sky.
http://www.freesat.co.uk/
http://www.freesatfromsky.co.uk/
http://www.ses-astra.com/landingPage/uk/index.php
http://www.lyngsat.com/28east.html