The Convert.ToInt32 is actually implemented the following way...
int.Parse(value, CultureInfo.CurrentCulture);
...which is the same as your stated alternative except it takes into account the culture settings. The int.Parse method is itself implemented the following way...
Number.ParseInt32(s, NumberStyles.Integer, NumberFormatInfo.GetInstance(provider));
...where Number is an internal class that you cannot call directly. The Number.ParseInt32 method is marked with the following attribute...
[MethodImpl(MethodImplOptions.InternalCall)]
...showing that it is implemented inside the CLR itself.