Yes, you are missing something very fundamental. The concept of grid cells and ice concentration. Remember grid cells are huge - NSIDC is 25x25 km2, and JAXA 10x10 km2. In each grid cell there can be a combination of (true) open water and (actual) ice floes. This is all represented by the sea ice concentration. Let's say of the 625 km2 of the NSIDC grid cell, 375 km2 is sea ice, and 250 km2 is open water - possibly as leads between the floes, or in some other distribution. Sea ice concentration in this grid cell will be 60% - 375/625. Sea ice extent for this grid cell will be the whole 625 km2 because concentration is above 15%.
Take an adjacent grid cell with 125 km2 of sea ice and 500 km2 of open water. Concentration is 20%, extent is 625 km2 (20%>15%).
In total we have 500 km2 of sea ice area, and 1250 km2 of extent, an average "compaction" ratio of 40%.
Now wind comes along and moves all the ice from the second grid cell to the first. Concentration rises to 80% (500/625), while in the second grid cell it drops to zero. Sea ice area remains 500 km2. However extent drops to 625 km2, a 50% reduction. This is a pure compaction event - no area was lost, but extent dropped sharply.
In another example, the weather melts 125 km2 of the 375 km2 of ice in the first grid cell. Sea ice area goes down by 25% (total of 375), extent remains the same (1250). Pure melt event.
In a third example, wind moves the ice from the second cell to the first, and weather melts 250km2 of ice. Total ice area is now 250 km2 (125+375-250) and extent is 625 km2. Average ratio is again 40%. Both have gone down by 50%. This was a melt + compaction event.