To my knowledge, the American call option on a non-dividend paying stock has the same value as the European call option.

Why does it happen then that according to Mathematica they are not equal?

FinancialDerivative[{"European", "Call"}, {"StrikePrice" -> 100.00, "Expiration" -> 1},  
    {"InterestRate" -> 0.03, "Volatility" -> 0.2, "CurrentPrice" -> 100, "Dividend" -> 0.0}]

Out[5]= 9.4134

FinancialDerivative[{"American", "Call"}, {"StrikePrice" -> 100.00, "Expiration" -> 1},  
    {"InterestRate" -> 0.03, "Volatility" -> 0.2, "CurrentPrice" -> 100, "Dividend" -> 0.0}]

Out[5]= 9.24515

Next question:

The numbers of "Steps" in the following specification is some sort of placebo, right?

FinancialDerivative[{"American", "Call"}, {"StrikePrice" -> 100.00, 
"Expiration" -> 1},  {"InterestRate" -> 0.03, "Volatility" -> 0.2, 
"CurrentPrice" -> 100, "Dividend" -> 0.10}, Method -> "Binomial", 
"Steps" -> 200]