The degree of access to the EU market. Which is effectively a tradeoff of access to market for sovereignty. Ie if you implement all EU laws (even though you have no say on them), you are EU compatible and will be given access. That's basically where Norway is. There are legitimate concerns of which is worse between loosing sovereignty over loosing the single market access.

In the extreme:

Weak = become like Norway or Switzerland; technically not in the EU, but bound to many of its treaties. Get you the benefits of, say, open borders, but also means paying for, say, saving the banking system and (almost) accepting whatever new rules the 'real' EU counties come up with (because it got exemptions for lots of EU regulations, Great Britain currently is almost less of a EU member than Switzerland, so it probably wouldn't go that far)

Strong = break all ties with the EU. No open market, border controls everywhere (including the border between Ireland and Northern Ireland) but also no more payments to the EU, and having the freedom to, say, create import tariffs for German cars.

"Hard Brexit" = there is no deal and commerce between the UK and the EU revert to WTO rules by default.

common market access and freedom of movement, mostly. a hard brexit means (potentially) sacrificing the former to reject the latter. a soft brexit means conceding freedom of movement to ensure continuity of economy

Hard versus soft, in other words.

The potential for compromise