Grading strip cards (i.e., and other hand cut cards) is all about minimum size requirements by PSA (and also by SGC). If the cards are cut too close to the inside border like the first card you have, it will never receive anything other than Authentic. If the card does meet the size requirements and does not break into the inside border, then it would receive miscut by PSA due to poor centering which you got on your second. For PSA, in addition to size requirements, the card must still be cut somewhat properly like a "square" card. For example, in the first card below, the card is cut badly. That is why even though it met minimum size, it still got an Authentic. However, the same card is in the second holder after I cleaned up the trimming with some nice scissors. (and I still own the card). SGC tends to be a "little" more lenient with this even though they care about size requirements also. If the card still has good eye appeal, they may still give it a number grade even if the border of the card breaks through the inside border. For an example, see this listing on a Big Head Ruth that slightly breaks into the border on the top left corner.
Link (I don't own that card.)
Note that for the cards above, there is no predefined outside border. Since there is no outside border, the cards can vary side to side or up and down. However, for the card below, there is an outside border on three of the sides (except the top). If there is an outside border, the cut must also typically show the outside border in addition to meeting the minimium size requirements. If there is no outside border, then the card just needs to meet the minimium size requirements, not break into the inside border and be somewhat "square."