Field rounds are much like target but over variable terrain. Different ages/disciplines shoot from different pegs. A set number of arrows are shot. The distances are either specified or unknown. In theory the score from roundels should give the best estimation of the best archer due to the fine graduations of the scoring.
However the 'unknown-ness' of the distances is limited as particular faces only appear at different distance ranges and the fixed target diameters lend themselves to distance estimation strategies. Also the multiple arrows from the same peg allow the archer to fix errors in subsequent shots. So it's not really a representation of any sort of archery in any sort of historical or hunting setting; it's target on a slope.
That's not a criticism; just a statement of opinion.
Animal faces are an attempt to simulate archery in a hunting scenario.
Animal faces tend to be shot from pegs in progression, red furthest, then white and blue. You can score a kill or wound. If you miss from one peg you advance to the next. Points scored go down according to distance shot and whether a kill or wound. No, when hunting, an animal would not hang around on a miss, but because the pegs are changing they are effectively new targets each time. But then an animal wouldn't stay still while you got organised and estimated range either
Unknown distances are much more unknown because you have much less of an idea how big the faces are so you have to genuinely estimate distances.
However there are loads of different shooting and scoring schemes and sometimes schemes are made up on the spot for different circumstances.
Both are fun in their own way and it's worth trying them both.