Are these close-ups or macros?

This is a subject that, like equivalence, can produce repeated, lengthy and sometimes acrimonious arguments. A lot of the time it revolves around the "true/correct/proper" definition of "macro". The most often used definition is that a capture is a macro if the size of the image of the subject on the camera sensor is the same size or larger than the size of the subject itself. This is known as being "at least 1:1".

In comparison, "1:2" means that the image on the sensor is 1/2 the size of the subject, while "2:1" means that the image on the sensor is twice the size of the subject.

To my way of thinking this definition has the merit of being unambiguous, well-defined, precise and fairly easy to understand. Also, to my way of thnking, it has the disadvantage in certain (rather common) circumstances of being not terribly useful and/or being very misleading. This has to do with sensor sizes.

Let's just consider 1:1 for the moment. A capture is or is not 1:1 irrespective of the sensor size. If the same subject is captured 1:1 on a large sensor and on a small sensor then you will see more of the subject on the larger sensor, but if you look at an area on the larger sensor the size of the smaller sensor you will see exactly what the smaller sensor would capture for that area.

This is sometimes known as "1:1 is 1:1" or similar, often coupled with something like "It is either macro or it isn't. Sensor size doesn't alter that."

Using the 1:1 definition of macro, I wouldn't disagree with any of that. 

However, the 1:1 definition also means that the image on the top left below is a macro and the one on the top right isn't, and that the two images below them are not macros either (none of these is cropped btw).

The reason for this is that the image at the top left was captured with a 60mm macro lens operating at 1:1 on a Panasonic G80, which has a sensor around 18mm wide. Since it was operating at 1:1 the scene was around 18mm wide. The image at the top right was captured with an FZ330 bridge camaera with a Raynox 250 close-up lens. The FZ330 has a sensor around 6mm wide. Since the scene was 18mm wide, the image on the FZ330 sensor  was only 1/3 the size of the scene, and so this was not a macro as the magnification was only 1:3. The other two, closer-in, shots were also captured with the FZ330 and Raynox 250, and neither of those two scenes is as small as 6mm wide (the smallest one, at the bottom right, was around 9mm wide. An image captured with the FZ330 would only be 1:1 if the scene was 6mm wide or less, so neither of these was a macro.

When different sensor sizes are involved (and I use four different sensor sizes) I think talking in terms of images being 1:1 macros or not is not very helpful, and tends to confuse the issue. I therefore prefer to talk in terms of scene widths and the kit needed to be able to photograph those scene widths rather than whether the required magnification is 1:1, 2:1, 1:2 or whatever. 

I also don't see much benefit in talking of images being macro or not based on the 1:1 definition. In my own mind I use much looser definitions of macro and close-up. I rather liked one of the descriptions I read on one of the forums, along the lines of "If it fits on the tip of your finger it is a macro. If it fits in the palm of your hand it is a close-up." If people want a size to think about I sometimes suggest that if the scene is less than an inch or so across it is a macro, otherwise it is a close-up. For my own photos I tend to think of my invertebrate photos as macros and my botanical images as close-ups. Sometimes I just refer to my photos as close-ups and leave it at that.

I don't think there is much benefit in arguing about what macro "really" means.