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Say, I use a thumbnail photo, as a smaller or cropped version of the original photo on a site/blog. The thumbnail is used as a preview to the post/article that has the full photo along with the original photo and credit/source of that photo.
Since the full photo is already credited in the post details, do I also need to credit the thumbnail?
That's assuming of course that I am allowed to use that photo to begin with as long as I credit the source/author.
Several court cases have held that using thumbnail images is fair use when:
Here is an article written by a lawyer that lays it out in more detail: http://garson-law.com/thumbnail-images-infringement-or-fair-use/
As far as crediting the thumbnail, when you use something under fair use, you are not required by law to credit that usage. See http://cmsimpact.org/resource/fair-use-frequently-asked-questions/ That article suggests that credit is important to artists and it is good etiquette to provide the credit. I'd say that your link to the original would satisfy most creators' desire for credit.
This answer was written with US law in mind.
The above answer from @Stephen Ostermiller is incorrect. ANY use of an image that is unauthorized, regardless of size, is copyright infringement and you would be liable for damages. If you don't believe me, call any copyright lawyer and tell them someone is using your images as thumbnails on their website and you want them taken down and the lawyer will offer to take your case and send DMCA takedown requests. The only instance where you can get away with it is when users of your website are uploading the images and you have a DMCA section on your site that explains what a copyright owner must do in order to have the image removed. This is because your website is crowdsourced. If you, however, are the one posting the image, you are not protected by DMCA. The only reason large websites like Google and Pinterest get away with it is because they have a lot of money to sink into legal fees and most copyright owners don't. Even if the images are crowdsourced, you can be held liable for damages since you are using the image commercially. The only way around this is to not monetize your site.
Source: https://www.copyright.gov/fair-use/more-info.html
Regarding using the item in a commercial sense, the weight of using it in a commercial sense, and of course determining damages (although, yes, damages are an afterthought), here is an excerpt from the above government URL (my emphasis is bold):
Fair use is a legal doctrine that promotes freedom of expression by permitting the unlicensed use of copyright-protected works in certain circumstances. Section 107 of the Copyright Act provides the statutory framework for determining whether something is a fair use and identifies certain types of uses—such as criticism, comment, news reporting, teaching, scholarship, and research—as examples of activities that may qualify as fair use. Section 107 calls for consideration of the following four factors in evaluating a question of fair use:
....
Effect of the use upon the potential market for or value of the copyrighted work: Here, courts review whether, and to what extent, the unlicensed use harms the existing or future market for the copyright owner’s original work. In assessing this factor, courts consider whether the use is hurting the current market for the original work (for example, by displacing sales of the original) and/or whether the use could cause substantial harm if it were to become widespread.
Clearly, the DMCA says that commercial use has an impact on the decision if the impact on the original copyright owner's business without permission is apparent. And what plaintiff wouldn't argue that?
