en_tn_lite_do_not_use/heb/11/13.md

without receiving the promises

This speaks of promises as if they are objects that a person receives. Alternate translation: "without receiving what God had promised them" (See: rc://en/ta/man/jit/figs-metaphor)

they saw and greeted them from far off

Future promised events are spoken of as if they were travelers arriving from far away. Seeing and greeting the promised events is a metaphor for believing and being glad that the events will happen. Alternate translation: "they believed and were glad about what God would do in the future" (See: rc://en/ta/man/jit/figs-metaphor)

they were foreigners and exiles on earth

Here "foreigners" and "exiles" mean basically the same thing. This emphasizes that this earth was not their true home. They were waiting for their true home that God would make for them. (See: rc://en/ta/man/jit/figs-doublet)