Essentially, one is a simple transactional email while the other is a drip marketing campaign that begins with a transactional email.
A welcome email serves to do just what it implies, welcome your subscriber to your email list. This email is likely triggered by an action that the subscriber has just taken, such as completing and submitting a signup form. There is typically only one email that does not invite a response from the subscriber. This is what makes it a transactional email.
On the other hand, a welcome flow is designed to both welcome the subscriber as well as provide information and content over a period of time. The flow may begin with a transactional email that is sent once a subscriber signs up, but it then continues on after the initial welcome email. The entire flow can consist of a number of emails and messages scheduled to be sent over the course of several hours or days.