Lognormal versus Black-Scholes Framework

This question is related to Monte Carlo Valuation, but will probably help me in understanding Lognormal since I don't

Suppose we have this setup

S = 45
Delta = .05
Sigma = .2
Alpha = .15
R = .04
European Put
K = 50
T = 4
We're simulating with 4 uniform #s .2, .6, .3, .8

Find current value of option using these 4

The question is: what is the difference between if the stock follows a lognormal model versus the Black-Scholes framework?


Lognormal versus Black-Scholes Framework