The Pilgrim commemorative half dollars were struck for in two years, 1920 and 1921. The final distribution figures for the 1921 were considerably less than the 1920; 152,112 for the 1920, and only 20,053 for the 1921. According to Dave Bowers, the 1921 was the first commemorative "variety" "specifically created to increase sales to collectors." But sales of the 1921 Pilgrims were much smaller than the 1920, perhaps because of the economic recession of 1921, perhaps because a lot of collectors already "had" a Pilgrim.
If you look at the PCGS Population Report, there appears to be about twice as many 1920 Pilgrims as 1921's. My experience is that there man be three or four times as many 1920's as 1921's, but not seven times as many as the distribution figures would suggest. Interestingly, in Gem condition, the 1921 Pilgrim is only a little rarer than the 1920. Where there is a definite difference is in lower, circulated grades. Many 1920 Pilgrims went into circulation and many circulated survivors exist today. For the 1921, while not as impossible to find in circulated grades as many of the 1933-1939 era commemoratives are, circulated examples are few and far between. All of this suggests that both years were sold to collectors, dealers, and speculators, but only the 1920's were placed into circulation.
The typical 1921 Pilrim is well-struck and marks are not usually a problem. Luster is of the frosty type and various degrees of toning can be seen. The average grade is MS63 to MS65.