Receiving requests to link to articles from my blog

[minicorrect]

I am still a novice in the blogging world and have no idea how to respond when someone contacts me through my blog suggesting I link to their "article that aligns well with my blog", such as:
"We recently published an article that you may be interested in entitled, ?XXX".I thought perhaps you'd be interested in sharing this article with your readers? After having followed your blog for a while, I feel that this one article would align well with your blog's subject matter."

Is this how sponsored/paid links come about? Or is this something different? If I were to read the article, like it and link to it, how would I do it as it would align with a post but not my entire blog? Would it be done as a guest post?
I apologise for my naivety, but I read lots of blogs that refer to being paid to write a post, etc but have no idea how they form those links in the first place.

I would dearly appreciate some pointers from more experienced bloggers who know and understand how this side of blogging works!!

I get these all the time and I bin them straight away. The point of these is the link, as the more links there are going into a site the better. So if I can get 20 people to link to my blog post/article, then Google will think my site must be authoritative/worthwhile and my site will then do better in search engines. The person emailing you will probably wrap it up in a whole load of schtick about them being a keen writer and the article being a great fit, but ultimately it's all about them securing a link.

Links from your site have a value, and this is why there's a market in selling them, and why you're being asked for one. However, the person who's asking you probably isn't prepared to pay. I know some bloggers respond to requests like this by sending their rate card, and very occasionally do manage to get some money for the link. But personally I don't think it's a very good use of my time and in any case I'm not really interested in selling links. Hence they go straight to the rubbish bin. I also have a line on my disclosure page which says: I do not place links for brands/services for free so please do not email me with proposals of this nature.

Thank you so much! I had a feeling this is what it was - simply people trying it on, and didn't want to respond inappropriately, but at the same time, don't want to be rude and ignore genuine enquiries.
It's only really now I'm getting into blogging a bit more that I've realised (from reading other blogs) that people will pay money for you to link to their company/site. I've been reviewing things I love just for the hell of it, unaware that these may come across as undisclosed sponsored links!
I have to admit I can't believe how much more there is to blogging than I thought when I started! I don't think I'll ever truly "get it"!