Did Jesus really face every kind of temptation that people face?
Yes. The context states that Jesus tasted every temptation that is common to man, and His temptations are seen in the Matthew account. The same three areas—the lust of the eye, the pride of life, and the lust of the flesh—are what mankind still confronts, confirming He faced the common temptations people face.
Les explains that Eve's temptation was threefold: the natural appetite was in high gear because she was hungry, the fruit was beautiful and appealed to the eye, and Satan promised she would be wise as God, appealing to pride. Those are the same three areas—lust of the eye, pride of life, and lust of the flesh—that mankind still confronts. The teaching then says Jesus tasted every temptation as was common to man, and those temptations are seen in Matthew. So His temptation covers the categories people face.
For we have not an high priest which cannot be touched with the feeling of our infirmities; but was in all points tempted like as we are, yet without sin.
Then was Jesus led up of the Spirit into the wilderness to be tempted of the devil.
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In what sense did Jesus experience every temptation?
When Scripture says Jesus tasted every temptation, it means He experienced every category of temptation, not every individual temptation a person faces.
How can Jesus have tasted every temptation if He did not face each individual one?
Jesus tasted every temptation not as individual temptations but by categories, because every temptation belongs to one of the three categories.
How can Hebrews 4:15 say Jesus was tempted in every way if He did not face every specific temptation?
Jesus experienced every temptation not individually but by category, so Hebrews 4:15 is true that He was tempted in all ways we face.
What is the difference between Jesus' temptations and our temptations?
The difference between Jesus and us is that He was tempted in all points just as we are, but whereas we fall into temptation, He did not fall.