"Check" or "check in on"

This verb, "to check", really confused me. Here's what I have found so far:

"check" in the meaning: to examine something to see if it is correct, safe or acceptable (source: Oxford Learner's Dictionaries)

Check your work before handing it in.

"check in" [US] to find out or report the status of someone or something especially as part of a regular pattern of communication or monitoring (often followed by on or with) (source: Merriam-Webster)

We access our work email on our phones, catch up on messages during our commutes and even when we're out at lunch, check in on work before bed—some of us feel like we have to just to be good employees.

https://youtu.be/dQVzxFh9yBc?t=957 (15:57)
https://youtu.be/0_dlGmwMywY?t=39 (0:39)

What is the difference between the two verbs with the meaning "examine things" in all these cases? Is it possible to replace "check in on" with "check" and vice versa in the examples above?

Solution 1:

In your context, you are dealing with two quite separate verbs:

To check transitive^1, = to ascertain if something is correct.

To check in (phrasal verb) intransitive = to arrive for the purpose of contact. ("in" is an adverb.)

To introduce their complement, intransitive verbs need a preposition, which has a noun phrase as its object:

I checked in(adv.) on(prep.) John(NP).

^1,To check is, technically, ambitransitive, i.e. an object may not appear but can always be implied.

Solution 2:

Cambridge Dictionary makes this sense of check in clear:

check in [contact]:

to contact someone by making a phone call, short visit, etc, usually in order to make sure there are no problems or to tell them that there are no problems:

• My son checks in regularly with me when he's travelling.

M-W goes straight to the purpose of making contact, which is unhelpful.

It does however add the useful 'often used with on or with'.

Typical examples:

• I'll check in on my grandad on the way home to see if he needs anything from the shops.
• I'll check in with the lab to see if the new phials have arrived yet.

....

Check is easily researched.