I am concerned that the second plant, a volunteer, could be this notorious invasive species called "tree of heaven"?

Container plant and a "volunteer".

Norfolk island pine (I think?) and....I don't think it's tree of heaven but I don't know what it is.

Second plant has doubly-compound leaves, which is not Ailanthus. Honestly, I'm not sure what it is. Might be Hercules Club (Aralia spinosa), but leaflets don't look quite right.

Possibly a Koelreuteria paniculata(Golden rain tree) or one of it's cousins.

Considered invasive in some of the warmer climates.

we might narrow it down. if you include your location in every post ...

the norfolk is a common houseplant up north ...

ken

@ken_adrian Adrian MI cold Z5

We are in San Diego.

The latter is possibly the invasive Melia azedarach with its twice compound pinnate leaves. Here's a link http://ucjeps.berkeley.edu/eflora/eflora_display.php?tid=33069

It is certainly invasive, we killed it so many times yet it kept on growing back!

Your invader is pretty enough. Looks like a terrible location for a tree though!

In my area (SF bay), every once in a while you see a giant Norfolk pine in someone's yard. They are pretty impressive trees!