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Recently we can see a wave of informal language that is used across websites over the Internet. However, the language used is not impolite. Maybe it's because of the marketing issues, or stuff like that. But it's definitely polite, and non-offensive, and at the same time it's not a formal language.
In other words, we might describe it using two simple attributes: informal & polite
Do we have a specific name for it. I was thinking of vernacular, but I'm not sure if it applies or not.
The short answer to your question is that no single term exists to describe the "informal [but polite] language that is used across websites over the Internet" nor informal/polite language in general.
However, as jlawler has pointed, in sociolinguistics the technical term for a manner of speech is "a register". Basically, humans change the way they pronounce words, the words they choose, and even the grammar they use based on who they are speaking to and how they wish to be perceived. I would suggest reading Language Style as Audience Design by Allan Bell for a more detailed analysis.
As for your question, if you wish to perform a detailed analysis you could define "a polite but informal register of speech commonly used on webpages" and then give examples showing the main traits of this register. If you simply want to refer to generic polite but informal speech you can simply refer to a generic "polite but informal register".
One final note is that I have seen some publications use the word "code" instead of register (as in code-switcing) but I'd suggest sticking with register since it seems to be the more common word these days.
