I don't think you're going to find a strict technical distinction that is consistently applied. Both 'Buffe' and 'Bevor' generally refer to defenses for the lower part of the face. You often find the term 'buffe' in 16th century contexts, and 'bevor' in 15th century contexts - but the latter word survives into the 16th. In the 15th century 'bevor' refers to the lower face defense worn with sallets and kettle hats. In the 16th century 'buffe' refers to much the same defense worn with burgonets. The immobilizing buffe mentioned in this source takes its form because of the style of joust it was made for, and this is not a characteristic of 'buffes' generally. Though I am not acquainted with this particular form of joust, the rennen family of jousts in general featured very heavy dully pointed lances and very thick helmets with bevors (or if you prefer, buffes) bolted or screwed to the breastplate. So this is not the difference.

For an example of buffes that did not immobilize, here is a burgonet with a 'falling' buffe which could be lowered for better breathing a visibility.

For an example of a very late 16th/early 17th century use of the word 'bevor', here is Shakespeare - Horatio describes the ghost of Hamlet's father, who was armed in full armour:

HAMLET From top to toe?

MARCELLUS BERNARDO My lord, from head to foot.

HAMLET Then saw you not his face?

HORATIO O, yes, my lord; he wore his beaver up.

HAMLET What, look'd he frowningly?

HORATIO A countenance more in sorrow than in anger.

HAMLET Pale or red?

HORATIO Nay, very pale.

HAMLET And fix'd his eyes upon you?

HORATIO Most constantly.

Since Horatio sees the ghosts face with the bevor up and not down (as it would be with a falling buffe) this very late example of the word may refer to some other face-covering - Blair refers to the upper part of late 16th century close helmet visors as the 'upper bevor' though he gives no source for this (and the bottom part of the helmet's face defense, covering the chin, is the 'bevor'). So it is possible that in the later 16th century 'bevor' had come to mean something different.

But as I said in the beginning, you are not going to see a strong distinction between these words, except for when they were most commonly used.