|Hi, are you asking how to distinguish from a user perspective if a client login site is an intranet or Internet site?|
If you are an employee with authorization to access the intranet, often times an intranet server may have a better response time than a public Internet site because there is presumably less traffic and factors that would slow down the network access. However, performance time is not necessarily a reliable indicator for a user to distinguish if they are logging on to an intranet or Internet site.
Usually intranet sites are typically designed to be more utilitarian with less graphic design elements, whereas Internet sites tend to have designs that are aesthetically pleasing with many graphic design elements. That's largely due to the fact that intranet sites are usually designed for internal company employees where as Internet sites are designed for the company's target audience in the public arena. Having said that, typically the larger the company, the fancier is the design for the intranet, so once again, this is not a reliable indicator.
If you have separate URL addresses and/or servers for your intranet than your Internet site and your client knows which URL is which, then this would be one potential identifier.