.NET and COM (ActiveX) objects perspective

string is an alias in C# for System.String.
So technically, there is no difference. It's like int vs. System.Int32.

As far as guidelines, it's generally recommended to use string any time you're referring to an object.

e.g.

string place = "world";

Likewise, I think it's generally recommended to use String if you need to refer specifically to the class.

e.g.

string greet = String.Format("Hello {0}!", place);

This is the style that Microsoft tends to use in their examples.

It appears that the guidance in this area may have changed, as StyleCop now enforces the use of the C# specific aliases.

Whereas one approach is to implement the ICloneable interface (described here, so I won't regurgitate), here's a nice deep clone object copier I found on The Code Project a while ago and incorporated it into our code. As mentioned elsewhere, it requires your objects to be serializable.

using System;
using System.IO;
using System.Runtime.Serialization;
using System.Runtime.Serialization.Formatters.Binary;

/// <summary>
/// Reference Article http://www.codeproject.com/KB/tips/SerializedObjectCloner.aspx
/// Provides a method for performing a deep copy of an object.
/// Binary Serialization is used to perform the copy.
/// </summary>
public static class ObjectCopier
{
    /// <summary>
    /// Perform a deep copy of the object via serialization.
    /// </summary>
    /// <typeparam name="T">The type of object being copied.</typeparam>
    /// <param name="source">The object instance to copy.</param>
    /// <returns>A deep copy of the object.</returns>
    public static T Clone<T>(T source)
    {
        if (!typeof(T).IsSerializable)
        {
            throw new ArgumentException("The type must be serializable.", nameof(source));
        }

        // Don't serialize a null object, simply return the default for that object
        if (ReferenceEquals(source, null)) return default;

        using var Stream stream = new MemoryStream();
        IFormatter formatter = new BinaryFormatter();
        formatter.Serialize(stream, source);
        stream.Seek(0, SeekOrigin.Begin);
        return (T)formatter.Deserialize(stream);
    }
}

The idea is that it serializes your object and then deserializes it into a fresh object. The benefit is that you don't have to concern yourself about cloning everything when an object gets too complex.

In case of you prefer to use the new extension methods of C# 3.0, change the method to have the following signature:

public static T Clone<T>(this T source)
{
   // ...
}

Now the method call simply becomes objectBeingCloned.Clone();.

EDIT (January 10 2015) Thought I'd revisit this, to mention I recently started using (Newtonsoft) Json to do this, it should be lighter, and avoids the overhead of [Serializable] tags. (NB @atconway has pointed out in the comments that private members are not cloned using the JSON method)

/// <summary>
/// Perform a deep Copy of the object, using Json as a serialization method. NOTE: Private members are not cloned using this method.
/// </summary>
/// <typeparam name="T">The type of object being copied.</typeparam>
/// <param name="source">The object instance to copy.</param>
/// <returns>The copied object.</returns>
public static T CloneJson<T>(this T source)
{            
    // Don't serialize a null object, simply return the default for that object
    if (ReferenceEquals(source, null)) return default;

    // initialize inner objects individually
    // for example in default constructor some list property initialized with some values,
    // but in 'source' these items are cleaned -
    // without ObjectCreationHandling.Replace default constructor values will be added to result
    var deserializeSettings = new JsonSerializerSettings {ObjectCreationHandling = ObjectCreationHandling.Replace};

    return JsonConvert.DeserializeObject<T>(JsonConvert.SerializeObject(source), deserializeSettings);
}