Kind of yes, but it's a bit more complicated than that, as you would expect from F1.

For 2016 there are 3 different tyre compounds available for each race, last season there were just 2.

The tyre manufacturer, Pirelli, will decide which 3 are available for each race, it varies from track to track.

There are a total of 5 compounds for them to choose from, ranging from Ultra Soft through Super Soft, Soft, Medium and Hard.  Generally speaking, they will choose harder compounds on tracks that are more "abrasive" ie harder on the tyres and vice-versa. 

The softer compounds give more grip and so are in theory quicker, but they also wear out more quickly and so the driver will need to pit more frequently if they use the softer compounds.

All drivers MUST use at least two different compounds during the race, unless it is classified as a wet race.

If it's wet, they can also choose Intermediate tyres, Wet tyres or Monsoon Tyres, depending on how wet it is.  They can also choose from the usual "dry" compounds if they feel the track is dry enough.

For each race weekend, each driver has a total of 13 sets of tyres, across the 3 compounds for that race.

The reason for the changes is to try to make the racing more exciting by giving the teams more options for strategy in the race, varying number of pit-stops etc.  I will not comment as to if that has worked or not though!

The teams will evaluate the tyres during the practise sessions and then call them "Prime" and "Option" based on their findings.  Usually the Prime tyre is the one they intend using for most of the race but this can vary if the track is "rubbered in" more than expected as the tyres will then last for longer.

More info here:

http://www.autosport.com/news/report.php/id/122220