There seems to be at least two types of using "Not that....". And my question is: what does "not that" mean in its second type of usage.

In the first type, "not that" is followed by a structure-complete sentence or expression. 

Example 1

*I've been teetering down my twittering and self editing my Facebooking lately. It's not that I don't have the urge to write things. It's just I have to fight the urge to write really inappropriate things that maybe my old High School English teacher doesn't really need or want to know.*

Example 2

*It’s not that I don’t care about football. I just don’t care enough*




In the second type, "not that" is followed by a object-missing expression.

Example 3(from Fringe)

*Olivia: Anything to do with metamorphic ability? Peter: Not that I can tell*

Here, tell is a transitive verb and its object is missing.

Example 4 (from Fringe)

*Olivia: Were you involved in...? Walter: Not that I recall*

Here, recall is a transitive verb and its object is missing.


**I understand that, in the first type, "not that" sort of means "it doesn't mean...". But I'm not sure about the second usage, and I don't understand why the objects of the transitive verbs are missing**