Must I two-weapon fight with different weapon types or can they be matching?

I think I’m clear on two-weapon fighting (thanks to Two-Weapon Fighting & Bonus Action in 5e) except for one thing. The PHB says (p. 195):

When you take the Attack action and attack with a light melee weapon that you’re holding in one hand, you can use a bonus action to attack with a different light melee weapon that you’re holding in the other hand. [emphasis mine]

Does a “different” weapon mean a different type of weapon, or just a different physical instance of a weapon? In other words, can I fight with two shortswords (one in each hand), or would I have to use a dagger or some other type of light weapon in my off hand?