qiǎ is the older native reading and covers physical pinching/wedging:
卡住 (to get jammed — also pr. kǎzhù),
卡脖子 (to seize by the throat / choke off),
卡壳 (gun jams; speech falters). It also names anything that pinches a flow of people:
关卡 (checkpoint),
哨卡 (sentry post),
边卡 (border post) — plus small clamp-objects:
发卡 (hair clip),
卡子 (clip; clasp).