new popups saying the web site is not secure

Based on the various responses, I have not communicated well. I'm going to try again using an example from just now. I opened an e-mail I received from Nespresso, where I order coffee. These are routine emails that I receive periodically--I signed up for them. When I open the email on my iPhoneX, the graphics do not display properly--it looks like this:

When I click on the spot where the graphics should be, I get this popup:

Then I went to Mail on my Mac. When I open the e-mail it looks like this:

When I click on the graphics in the message, it takes me straight to the website with no problem and looks like this:

This is the same e-mail and the same website. This happens somewhat frequently on my phone.

In addition, yesterday I received the same popup on my Mac when attempting to access well-known websites using Safari. It did not happen every time, but it did happen. I did not take screenshots at the time, except for the one at the top of the page. So probably best that I keep my question to the first part of this message.

My iPhone has trouble displaying some emails and opening some hyperlinks on Safari from previously used web sites from well-known companies. My reference to Horchow in my very first question above is the same phenomenon. Same thing JUST happened with Starbucks.

Thank you very much for all the assistance.

My question is why have these pop ups started and how do I stop them from happening. In 90% of my emails, I can click links with no problem. For a few emails, I get the pop up. The messages are all from stores where I have signed up to receive emails. This only started happening in the last few months. Thank you.

I still don’t understand. They are the same link to the same web site in the same email, just viewed on two different devices. Why does my phone think it’s not private but my Mac thinks it is? And again, these are emails I signed up for from a site I have visited many times over the years.