What is the purpose of Coldfox?

1. To provide a no-hassle means of switching to a secure privacy focussed up-to-date browser
2. To restore the old fashioned logical arrangement of Tabs below the URL bar
(Historical note: The plunge of Mozilla Firefox losing 75% of their market share over the last decade started when they forced Tabs-on-top)
3. To be a truly fully portable browser with no install required, a self contained profile & cache.
4. To fight deplatforming and censorship as they are the most insidious threats to human rghts.

Updates are disabled by default. Can I still use mozilla update?

Yes, though you will lose some of the customizations preset in Coldfox

What about extension updates?

I did leave extension updates enabled for the moment due to developers still addressing security and bug issues after transitioning to the web extension format. These only ping once every few days and can be easily disabled in add-ons preferences

What do you mean when you say ALL telemetry is blocked?

Even after switching off telemetry from within the browser settings I noticed Firefox still generates at least one telemetry ping. Presumably this is an install ping as is sent by Chrome, Vivaldi et al. I disabled this via alternative means.
Automatic update checks cannot be switched off by the user. I also disabled this via alternative means.
The 'safebrowsing' updates to blocklist.xml contact google to download the list they maintain. Given their history users are more in need of being protected FROM google rather than BY google. Updates to this are disabled by default, as this connection involves identifying the user, their location, browser ID and IP to google. This blocklist is also another potential method of deplatforming alternative sites. The original blocklist is still enabled by default: You can examine its contents by opening app\Firefox64\browser\blocklist.xml

What about pocket and sync?

Pocket is disabled by default. You can reactivate it in about:config, though I have yet to meet a person who wants to use it. To use sync requires you to set up a mozilla account and log in. Without doing this it is inactive by default.

I want a firefox family browser that respects privacy: Should I use Waterfox or Coldfox?

You can always use both (I do). Both block telemetry. Being self-contained and Identifying to your computer as Coldfox, you can run it simultaneously with any other browser.

The basic differences are...

Based on Firefox56 with security updates patched
Has eme/drm content blocked
Still has the versatile XUL extensions
Has its own extensions store
Normal installation
Default skin

Based on latest Firefox
Will run eme/drm content
Privacy/security extensions installed by default and custom tweaked (NoScript/Adblock)
Uses Mozilla extensions store
No installation
Preskinned old style with a custom theme and extra search engines (also the dissenter extension)

In brief Waterfox has more versatile features but is slower and some websites won't work properly on the older firefox base. One of the motivations of creating Coldfox was to address that problem, so the two browsers compliment each other perfectly.