Unexpected identical solutions in solutions pool

I have a question about the solutions pool in Gurobi. In the code snippet below, I created an IP model with (a,b) = (1, 0) is the only solution. However, the model yields two identical (1, 0) solutions.

import gurobipy as gp
from gurobipy import GRB

model = gp.Model()
model.Params.PoolSearchMode = 2
model.Params.PoolSolutions = 2

vars = model.addVars(2, vtype = GRB.BINARY)
a, b = vars[0], vars[1]
model.addConstr((a == 0) >> (b >= 1)) # indicator constraint
model.addConstr(b == 0)
model.optimize()
print(f'\nSolutions count: {model.SolCount}')
for i in range(model.SolCount):
    model.Params.SolutionNumber = i
    print(f'Solution {i}: (a, b) = ({a.Xn}, {b.Xn})')

# Output
# Solutions count: 2
# Solution 0: (a, b) = (1.0, 0.0)
# Solution 1: (a, b) = (1.0, 0.0)

Are solutions in the solutions pool necessarily different? Is there any parameter that I can set to make sure the difference in the solutions pool?

One more thing is that if I change the indicator constraint to

model.addConstr((a == 0) >> (b == 1)) # it is (b >= 1) above

then the model yields only one solution, which is what I expected. It confuses me since b==1 and b>=1 are the same when b is a binary variable.

I'm using python 3.8 and gurobi 9.0.3.