Above, I’ve already outlined the first difference between the two: the group of recipients.
MLP is used by companies that want to enter a large, competitive market with an established user base. MVP is different because you use it to validate solutions that have never been created. MVP is to examine whether the world needs this certain feature at all.
This, in turn, makes both strategies differ in examining the user's needs.
When building an MVP, you don't need such a deep understanding of your audience's tastes; it’s enough to find out if they can solve a problem with your solution. You also don't have to worry about competition because there simply isn't any or is very little.
In the case of MLP, you need to deeply understand the characteristics of both the end user and your competition. Specific visual standards are already defined, so to stand out, you need to get to know them, e.g., by interviewing users or checking reviews of competing solutions.
The last difference, resulting from the previous two, is the design involvement in the development process.
When creating MLP, you will involve UI and UX designers to a greater extent than in the case of MVP, and you will release a more visually appealing product.