"Heal" vs. "mend": where meaning overlaps and diverges

What is similar?
Both "heal" and "mend" involve the process of making something damaged or broken whole again. They can refer to repairing physical damage or restoring well-being, and both can be used metaphorically to describe fixing emotional or relational issues.
What is different?
"Heal" typically relates to recovering health or well-being in living organisms, addressing physical wounds, illnesses, or emotional pain. "Mend" generally refers to repairing physical objects or materials that are broken or torn, such as clothing or equipment, but can also be used figuratively for improving situations or relationships.
Which one is more common?

Examples of usage
Heal- The doctor expects the wound to heal in a few weeks.
- Time can help heal emotional pain.
- Her kind words helped heal the broken trust between them.
- She used thread and needle to mend the torn dress.
- The mechanic mended the broken engine quickly.
- They worked hard to mend their strained relationship.