Can I use the same authentications of internal users (available in AD) to external users.?
If no what all authentication method I can use for external users?
Is there any difference in authentications from SP 2007 and 2010?
Is there any difference in authentication in SharePoint versions, that is foundation , standard and server.
There are many options for configuring authentication, depending on your requirements. You can of course use windows authentication and NTLM authentication to allow internal users to use their windows account to login. You can extend the web application to use windows authentication in an extranet zone. Then users outside the domain can be prompted to enter user credentials.
External users (eg. internet users) can use anonymous authentication to read public documents, or you could use SSL, Windows Authentication authentication and ISA to secure access to your SharePoint server externally.
SP 2010 includes Claims-based authentication. Claims-based authentication uses tokens to pass security information around. Here is an overview of claims based authentication: http://blogs.technet.com/b/ritaylor/archive/2009/06/03/claims-based-authentication-an-overview.aspx .
There is no difference between authentication methods from SP foundation and standard/enterpise, and WSS/MOSS. Here is a handy article on planning authentication: http://technet.microsoft.com/en-us/library/cc288475.aspx
SharePoint uses Zones to control access internally and externally. Authentication methods provide flexibility to authenticate users from inside and outside of a domain/enterprise network. However SharePoint also provides other functions to help manage authorisation and security of data (eg. Lockdown mode, which puts a site in readonly/access mode for internet access). Also, it allows people to access information with different security, based on authentication by extending web applications and having multiple authentication providers.
SharePoint uses standard ASP.NET authentication providers which means you can use SQL or other storage devices to manage users and roles using authentication.
You could use forms based authentication as well, which provides a login form within the browser to further extend authentication possibilities.
It is important to match security requirements with authentication providers.