Most airlines vary the number of frequent flyer points/miles you collect depending on the "fare class" of the ticket you purchase. Higher fare classes such as First Class, Business Class and sometimes "full fare" Economy will earn you more, whilst cheaper fare classes such as "discount economy" will earn you less.
In the case of BA, they have pages on their website that show the earning rates for other OneWorld airlines as well as their partner airlines. As you can see, for Finnair (as well as most other airlines), discount economy fares only earn 25% of the number of miles flown, so for a 1000 mile fight you would only earn 250 Avios points.
Whether you bought your tickets during a sale is not directly related, however it is indirectly relevant as it's normally the cheaper discount economy fare classes that are included in the sale, so presuming you're flying economy it's almost certain that any tickets bought during a sale would be in their "Economy (discounted)" tier, and thus only early 1/4 the miles on most airlines.
Finding the fare class of a booking will depend on the airline and how you're booking it. Some websites will clearly state the fare class during booking, some will only show it on your confirmation, and some may not show it at all. You're looking for something like "Fare Class : X" or possibly something like "Fare : XYZABC" in which case it would normally be the first letter of that string (ie, X).