The BSM model uses an underlying asset's implied volatility as an input but the binomial tree approach uses its historical volatility.

The binomial tree approach, but not the BSM model, assumes that the expected return from the underlying asset is the risk-free rate of interest.

In the binomial tree approach, delta is equal at each node since the probabilities of the price moving up or down during a period are constant and equal for both the underlying asset and the option.

If the assumptions of the BSM model hold, the implied volatility of a longer-term option and the implied volatility of a shorter-term option on the same underlying asset will be the same.