What we’re really talking about here are learning systems.
In simple terms they often both provide a similar capability. However, as is often the case, the devil is in the detail. Fundamentally, it will come down to the level of functionality and how much you want to be able to do with the system.
A portal is really just a way of viewing content. It’s a location where content is hosted or provided and, from which, you can view or possibly download it. Often it will also come with a level of reporting capability. Think of it like a library or a repository and you won’t go far wrong.
A Learning Management System or LMS is a far more comprehensive animal. These days some of them can do both learning activity and more general HR activities like performance management (some but not all). The LMS itself is an application, usually cloud-based, that captures all the information relevant to your learners. It’s a way of both administrating your learner population, whilst also providing them with access to the content itself. Of course, this is a very simplistic description and many of them can do a whole lot more.
Often customers start with a Portal and then, as they mature, they transition to an LMS when the functionality they require outstrips that of the Portal.