wow. easy to grasp but hard to explain evidently.
with an equipment freeze...yes, you can always be awarded a "higher- numbered equipment/pay band".
with a bidding freeze you cannot be awarded anything except a captain vacancy in current equipment, a "new" base (opened less than 6 months), or of course a lateral (same equipment/seat)
You incur a bidding freeze by bidding a vacancy that does not move you from a lower-numbered band to a higher-numbered band.
So yes, if you are a 737FO and you bid A320FO, you will incur a bidding freeze which will not allow you to be awarded a 777FO bid until you have served that freeze. You could be awarded a 320CA bid, however.
Clear as mud? Bid accordingly. Good day.