Greetings!
There are some very enlightening suttas in the Samyutta Nikāya which help shed light on vitakka-vicāra in the context of bhavana/jhāna.
SN 46.3 Sīlasutta
(...) Because after hearing the teaching of such mendicants, a mendicant will live withdrawn in both body and mind,
Tathārūpānaṁ, bhikkhave, bhikkhūnaṁ dhammaṁ sutvā dvayena vūpakāsena vūpakaṭṭho viharati—kāyavūpakāsena ca cittavūpakāsena ca.
as they recollect and think about that teaching.
So tathā vūpakaṭṭho viharanto taṁ dhammaṁ anussarati anuvitakketi.
At such a time, a mendicant has activated the awakening factor of mindfulness;
(...)As they live mindfully in this way they investigate, explore, and inquire into that teaching with wisdom.
So tathā sato viharanto taṁ dhammaṁ paññāya pavicinati pavicarati parivīmaṁsamāpajjati.
At such a time, a mendicant has activated the awakening factor of investigation of principles
As I tried to show in bold here, the word 'vitakka' is given in the description of sati (mindfulness/recollectedness), and the word 'vicara' is given in the description of dhammaviciya (investigation of dhammas). This fits in rather well also with the idea of "thinking and pondering," "directed thought and evaluation," "reasoning and deliberation," etc. We see 'vitakka' as the mind directed to a theme, thinking OF something, and 'vicara' pondering it, examining it, the mind 'wandering' with the theme (from the etymology of the word).
This also makes sense of some of the suttas such as AN 8.63, where there is an instance of the "3-way samādhi"; that is, with vitakka
and vicāra, without vitakka but with vicāra, and then without both vitakka and vicāra.
We also see in SN 47.10 for instance the difference between
"directed" satipatthāna practice to fulfill the bojjhangas -> samadhi/jhāna, etc., vs.
"undirected" practice. Directed practice is where one directs the mind to an 'inspiring theme' and thinks about it and evaluates/ponders over it, then once the mind is joyful and calmer, one withdraws the thinking and pondering, or directed thought and evaluation. Once the mind is no longer directly applying itself to think about the theme, it may still be doing some subtle pondering and deliberation/evaluation of the topic already established (avitakka, vicara), until that is stilled and the mind settles into 'noble silence' -> second jhāna.
This, of course, naturally makes sense of the use of vitakka-vicara in relation to jhāna and other suttas about thoughts. We have to direct the mind away from unwholesome thoughts, and direct the mind to think
about wholesome ones (MN 19, MN 20, etc.), and once the mind has been properly secluded from sensuality on the level even of thinking and is only thinking and pondering about wholesome things that establish sati, dhammaviciya, and lead to joy and calm, those thoughts are settled because they can make the body/mind tired (MN 19), and the mind can more easily settle into stable samādhi (2nd jhāna). This matches up with the Dantabhūmi sutta for instance as well (MN 125), where one transitions from the satipatthanas with thinking, to stilling the thinking and entering directly into 2nd jhāna.
It seems as others have said that 'examining' may (in some contexts) reflect the usage of vicara, though honestly I think "pondering" is a very down-to-earth, accurate translation. As soon as we go into "applied and sustained mental application," we've deviated from what these normal, everyday Pali words actually mean. They apply to meditation as is without needing to be filtered over with new meanings—something most of us probably agree upon. "Pondering," "examining," "deliberating," "turning over in the mind," etc. all are good for me. "Vitakka" seems to be more reasoned selection and direction of thought to things. I think about X, then Y, then Z. I think and 'hammer out' a view (as some suttas mention with 'takka').
I thought it was interesting and helpful to bring these things together. It's rather obvious that "vitakka-vicara" do not imply or ever mean something other than directing thought to ideas or topics/reasoning, and then the pondering/deliberation/turning over in the mind of that thought. It's nothing mystical or separate in relation to samādhi, and we see this same usage of the words align with descriptions of proper use of thought, and then stilling even wholesome thoughts: two themes very prominent in the suttas.
With mettā!