Assign taxonomy terms (ie tags) to a post in a specific order has no sense form me unless the taxonomy is hierarchical. The core tags taxonomy is no-hierarchical and category is hierarchical. So, you can define a hierarchical custom taxonomy or use the built-in category taxonomy.
Think in a natural flow of description terms. In a no-hierarchical context, what description term should be the first? There is no reason to put one over another, you can order them just like you can order a string. In a hierarchical taxonomy the order can be define as you want or need.