Are these molecular structures of cyclodecapentaene identical?
If you make spring-and-ball models of both compounds, you can see that the two compounds are entirely different, and both are contorted.

The all-cis model on the left has all its hydrogens pointing outward, so the contortions of the carbon chain involve just carbon-carbon twisting to come close to 120 degree angles. The model of the cis-trans molecule on the right has two inward-pointing hydrogens (all the rest point out) which are sterically interacting so much that they introduce strain that is not evident from the carbon-only diagram in the original post. (If I put in all the hydrogens, the image is too cluttered.)
The fact that one is all cis and the other cis-trans certifies that the molecules are different, but the 2-D drawing can seem vague. The NMR spectra of these two compounds would be different. I can imagine the molecule on the left flipping all around (the model sure did!), but the molecule on the right seems pretty stuck.
Thinking in 3-D is easy after you've done it many times. But when you are starting out, it is helpful to make molecular models. And even if you've done it a million times, there are situations where your mental image is so fluid that you need to solidify it with a model, no matter how inadequate the model is. And then you mentally add onto the solid model.