Context is king.
The people were in no doubt as to the cause for death in the camp, for they cried out: “We have sinned, for we have spoken against the Lord ...” (Numbers 21:7). The remedy was to look in faith upon a serpent of brass lifted up upon a pole.
What is the relationship between their sin, a serpent of brass and the Lord Jesus Christ?
Well the common denominator to both types, of faith in the snake and pole and Christ on the Cross is that both concerned people with their natural human bias or tendency to sin. This was the reason for their existence to know what sin causes, death, physical, mental and spiritual.
Further, the former could not take their sins away permanently, as they had to keep looking physically up to the snake, to maintain and keep them sinlessness in the eyes of the LORD and that was impossible to do. It was designed as an imperfect and temporary solution to their sin problem. The snake was an imperfect and tainted sacrifice and reflected the spiritual condition of those placing their faith in it. Imperfection having faith in an imperfect image or reflection that can never truly save anyone.
It was a crude learning and training ground if you will for mankind to know and depend on the LORD as their Saviour.
The latter could take their sins away permanently as those that believed genuinely could keep the spirit of Christ within themselves in heart and spirit as their Saviour . And they 'looked up' to him in faith, in spirit and mind. It was designed for perfection, permanent sinlessness and eternal life.