Chicago Manual of Style 16 (books) and AP Stylebook 2017 (media) agree unless noted.
e-book, e-business, e-commerce, e-reader, and other e-terms get a hyphen.
e-mail (Chicago style) But UPDATE! Chicago will be changing this preference to email for the 17th edition, due out in September 2017.
email (AP style)
e-sports (Chicago style)
esports (AP style as of June 2017)
the Internet (Chicago style) But UPDATE! Chicago will be changing this preference to the internet for the 17th edition, due out in September 2017.
the internet (AP style) 1
Rules apply for noun and adjective forms.
the net, net neutrality
the darknet, darknets (AP style) (Chicago does not cover this term.) The part of the internet accessible through encrypted networks and apps that provide anonymity.
the deep web (AP style) (Chicago does not cover this term.) The part of the web not searchable with search engines, as it exists behind passwords, firewalls, or other restrictions. This includes Facebook.
the World Wide Web
the web 1
website,2 webcam, webcast, webinar, webisode, webmaster
web address, web browser, web hosting, web-based publication
web page (Chicago style)
webpage (AP style)
webfeed (AP style) (not listed in WNW, MW11, or CMS)
blog or weblog (Chicago style)
blog or Weblog (MW11 entry)
blog (AP and WNW entry) (weblog is not listed in either)
bitcoin, 500 bitcoins This term is covered in AP Stylebook, but not in Chicago Manual of Style or either dictionary. AP began lowercasing it in 2014.
hot spot Both dictionaries and stylebooks agree, two words whether using the technological, scientific, literal, or figurative sense.
PC and PCs (for personal computer)
Wi-Fi Both dictionaries and stylebooks agree on capitalizing the W and F.
a Wi-Fi hot spot
For companies and brands with an initial lowercase letter but a capitalized second letter:
iPhone gains users. (Chicago style—do not capitalize first letter at beginning of sentence.)
IPhone gains users. (AP style—capitalize first letter at beginning of sentence.)
AP notes this rule also applies to the term iOS at beginning of sentence:
An update is available for the iOS app.
IOS app update available.
The web is a subset of the internet, and the two terms are not synonymous. The internet includes e-mail and other applications. The web refers to the service that allows multimedia documents to be published on the internet. See AP Stylebook 2017 under web and internet.
1 AP capitalized internet and web until June 1, 2016.
2 Chicago’s dictionary, MW11, lists website and Web site as equal variants. Chicago prefers website.
AP’s dictionary, WNW5, lists website, with web site and Web site as less common variants. AP prefers website.
3 Chicago’s dictionary, MW11, lists Weblog, but Chicago prefers weblog.
Sources: Chicago Manual of Style 16 and AP Stylebook 2017
Chicago style dictionary is Merriam Webster’s Collegiate Dictionary, Eleventh Edition (MW11)
AP style dictionary is Webster’s New World Collegiate Dictionary, Fifth Edition (WNW5)