My own preference would be to say Major 3rd or Major 3 or just 3 for Major, and b3 for a minor 3rd.
But
if it's already established which "mode" you're in, whether discussing scales or chords, just saying "third" would suffice.
But If you're discussing "mixing" Major and minor sounds together, being specific would be necessary.
Then again, you might be discussing a 3rd between 2 notes that don't involve the root.
It can also be confusing when people use interval (between 2 notes) and scale degree (1 note) interchangeably.
As in "play the minor 3rd" when meaning "play the b3".
And, as we usually discover, "convention" depends on the instructor.
Not all conventions are standard.
We gotta dance with who brung us.