I need help figuring out when you’re using text message.SMS will the other person receive that text message

SMS is a cellular protocol that does not provide read receipts or confirmation of a received message. If the message is undeliverable you will receive that message pretty quickly after attempting to send it and be given a chance to send it again.

If you are looking for a positive confirmation, such as a Delivered message you will need to use a different messaging protocol, such as RCS or iMessage. Both of those protocols will tell you when a message has been received. To get Read Receipts using those protocols, the recipient is the one that has to allow that as it is there personal choice if they want to let the sender know they have read the message.

More information about each of these protocols can be found here:

What is the difference between iMessage, RCS, and SMS/MMS? - Apple Support

Re: "I need help figuring out when you’re using text message.SMS will the other person receive that text message"

Assuming you are using a computer or device with the newest available compatible OS version: correctly addressed messages should generally get though ok.:

Basically: Apple to Apple devices use wi-fi to safely send encrypted iMessages (blue bubbles)

Apple to non-Apple devices must rely on SMS text messages (green bubbles) and provider charges may apply

For more info: Apple support's online article (link below) may help:

What is the difference between iMessage, RCS, and SMS/MMS? - Apple Support

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Re: "Will the other person receive that text message?"

Are you positive you will use all the correct details to contact the other person ?

Can you rely on your iMessage wi-fi provider and / or your SMS provider?

For letting others know you received their messages:

You can: Turn read receipts on or off in Messages on iPhone

Eg: says:

Get read receipts when someone else sees your messages

"You can’t turn on read receipts for anyone but yourself".

and

"To receive read receipts when your messages are opened, ask the recipient to turn them on. See Turn on read receipts for one person, ...."

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Re: " ... by the way this is really important"

Please let us know what you need, if you need more info.

or

Apple provides a Messages Support website )info. / support / contact options etc.)

Messages for iPhone, iPad, Apple Watch, and Mac - Official Apple Support