Let's examine what ILSpy says about these two...
public virtual int IndexOf(string source, string value, int startIndex, int count, CompareOptions options)
{
if (source == null)
{
throw new ArgumentNullException("source");
}
if (value == null)
{
throw new ArgumentNullException("value");
}
if (startIndex > source.Length)
{
throw new ArgumentOutOfRangeException("startIndex", Environment.GetResourceString("ArgumentOutOfRange_Index"));
}
if (source.Length == 0)
{
if (value.Length == 0)
{
return 0;
}
return -1;
}
else
{
if (startIndex < 0)
{
throw new ArgumentOutOfRangeException("startIndex", Environment.GetResourceString("ArgumentOutOfRange_Index"));
}
if (count < 0 || startIndex > source.Length - count)
{
throw new ArgumentOutOfRangeException("count", Environment.GetResourceString("ArgumentOutOfRange_Count"));
}
if (options == CompareOptions.OrdinalIgnoreCase)
{
return source.IndexOf(value, startIndex, count, StringComparison.OrdinalIgnoreCase);
}
if ((options & ~(CompareOptions.IgnoreCase | CompareOptions.IgnoreNonSpace | CompareOptions.IgnoreSymbols | CompareOptions.IgnoreKanaType | CompareOptions.IgnoreWidth)) != CompareOptions.None && options != CompareOptions.Ordinal)
{
throw new ArgumentException(Environment.GetResourceString("Argument_InvalidFlag"), "options");
}
return CompareInfo.InternalFindNLSStringEx(this.m_dataHandle, this.m_handleOrigin, this.m_sortName, CompareInfo.GetNativeCompareFlags(options) | 4194304 | ((source.IsAscii() && value.IsAscii()) ? 536870912 : 0), source, count, startIndex, value, value.Length);
}
}
Looks like it considers culture as well, but is defaulted.
public bool StartsWith(string value, StringComparison comparisonType)
{
if (value == null)
{
throw new ArgumentNullException("value");
}
if (comparisonType < StringComparison.CurrentCulture || comparisonType > StringComparison.OrdinalIgnoreCase)
{
throw new ArgumentException(Environment.GetResourceString("NotSupported_StringComparison"), "comparisonType");
}
if (this == value)
{
return true;
}
if (value.Length == 0)
{
return true;
}
switch (comparisonType)
{
case StringComparison.CurrentCulture:
return CultureInfo.CurrentCulture.CompareInfo.IsPrefix(this, value, CompareOptions.None);
case StringComparison.CurrentCultureIgnoreCase:
return CultureInfo.CurrentCulture.CompareInfo.IsPrefix(this, value, CompareOptions.IgnoreCase);
case StringComparison.InvariantCulture:
return CultureInfo.InvariantCulture.CompareInfo.IsPrefix(this, value, CompareOptions.None);
case StringComparison.InvariantCultureIgnoreCase:
return CultureInfo.InvariantCulture.CompareInfo.IsPrefix(this, value, CompareOptions.IgnoreCase);
case StringComparison.Ordinal:
return this.Length >= value.Length && string.nativeCompareOrdinalEx(this, 0, value, 0, value.Length) == 0;
case StringComparison.OrdinalIgnoreCase:
return this.Length >= value.Length && TextInfo.CompareOrdinalIgnoreCaseEx(this, 0, value, 0, value.Length, value.Length) == 0;
default:
throw new ArgumentException(Environment.GetResourceString("NotSupported_StringComparison"), "comparisonType");
}
By contrast, the only difference I see that appears relevant is an extra length check.