What is the difference between Lost Technica 《秘奥義【ロスト・テクニカ】》 and Last Crest 《魔道極法【ラスト・クレスト】》?


The terms Lost Technica 《秘奥義【ロスト・テクニカ】》 and Last Crest 《魔道極法【ラスト・クレスト】》 are
quite ambiguous, since they are usually mentioned together with the
explanation for being a member of Trinity Seven.

In chapter 17, both terms are used one after another near the end of the
chapter. This is from just before Liese activated her trump card.

> ["To be a Trinity Seven means that you've acquired the _Lost Technica_ in
> your particular archive." \- Liese](https://i.stack.imgur.com/0kcMz.png)
> [[Japanese version]](https://i.stack.imgur.com/xRCBi.png)

When Liese activated her trump card, and Sora (the human form of Astil
grimoire), warned Arata about the magic being used.

> ["This is Avaritia's _Lost Technica_ , the _Last Crest_ ..." \-
> Sora](https://i.stack.imgur.com/bzG1X.png)
>
> "That's right. It's _**Baal Peor**_ " \- Liese

Then in chapter 19, the condition to be part of Trinity Seven is reiterated,
but this time with _Last Crest_ in place of _Lost Technica_ :

> "The Trinity Seven are the top class magi of each of the seven deadly sins,
> right?" \- Arata
>
> ["Correct. We are the ones who have mastered the _Last Crest_ of each
> archive" \- Lilith](https://i.stack.imgur.com/g3fTz.png) [[Japanese
> version]](https://i.stack.imgur.com/1UVNE.png)

I have two questions regarding these two ambiguous terms:

  1. What is the difference between them?

  2. Regardless whether they refer to different concept or not, does _Lost Technica_ implies _Last Crest_ and vice versa?

(Please back up your answer with primary sources, rather than secondary
sources like Wikipedia or Wikia. You can use them as starting point, though).

