Well, in the meaning in common use in the BS7671 regulations, a connection is the joining together of conductors.
But there is no consistency of the use of that term with such a meaning in the document in question.
e.g.:
0.3 The diagrams in Appendix A give an
indication of the sorts of electrical services
encountered in dwellings, some of the ways
they can be connected..
b. permanent labels, for example on earth
connections and bonds...
3.11 In relation to ‘embedded’ generation, the
Regulations require persons operating ‘switched
alternative’ sources of energy in their installations
to prevent a parallel connection occurring with
the distributor’s network...
...heat-resisting flexible cables are required for
the final connections to certain equipment..
For the arrangement shown, this applies to the consumer unit and the wiring connecting it to the supplier’s equipment.
The thing exposed in this case, as you say yourself, is a cable, not a connection.
So there is nothing in the use of the words "connection", "connector", "connected" etc in Approved Document P which can lead you to (reasonably) think that "connection" can only mean "the joining together of conductors".
It may well be that the author of that document mis-interpretted the actual law,
There is no doubt that he did, because the actual law makes no mention of a distinction between exposed outdoor connections and none, no matter what "connections" might mean.
but the final meaning, however illogical, is clear.
It only seems clear to people who interpret it in an illogical way.
Firstly, as can easily be seen by reading the document, there is nothing in it which can lead you to logically think that "connection" can only mean "the joining together of conductors".
Secondly, if you
do think it means that, then what on earth is your interpretation of "exposed outdoor connections"?
A connection between conductors which is outdoors and exposed?
What you're doing is interpreting something in a way which is illogical and which leads to the situation where you think you could notify work which involved the installation of exposed connections between conductors.
Since you brought up the subject of what BS 7671 says about connections, maybe you'd like to read what 410.3.5 and 417 says about that.
If you'd suddenly like to forget BS 7671, maybe you'd like to consider if an exposed connection between conductors would comply with P1.
No - it's all crazy - the possibility that you might have "exposed outdoor connections" cannot mean that you might have "exposed outdoor connections between conductors". Such an arrangement would be so grossly unsafe - do you really think that the authors of AD P thought they needed to clarify the situation where you'd not done something grossly unsafe and illegal?