Fixed Target Number on Dice
Storyteller uses variable Difficulties (target numbers) that vary by circumstances.
In Storytelling, the target number you need to roll for a die to be counted as a success is fixed at 8, and any situational modifiers are applied to the total number of dice you roll (your "die pool").
In Storyteller, a botch is defined as rolling at least one 1, and either zero successes, or fewer successes than 1's, thus giving a possibility of a botch on any roll.
In Storytelling, a botch is only possible when rolling a Chance Die (when your pool has been penalised into the ground).
In the second edition of Chronicles of Darkness, (still called Storytelling just to maximize confusion) Dramatic Failures are available whenever you fail a Chance Die or whenever you simply fail a roll and you agree to take a DF in return for a fraction of an XP (a "Beat").
Storytelling tried to shift to a more uniform 3×3 matrix of attributes, cross-referencing power, finesse and resiliance against the physical, social and mental. Some attributes differ drastically as a result. Also, how some derivative characteristics are calculated or even what they are differs.
In Storyteller, using WP gives automatic successes.
In Storytelling, it provides bonus dice. Also, how the base Willpower rating is calculated or purchased varies.
Virtues in Storyteller are primarily a VtM thing, and are ratings.
In Storytelling, a Virtue and a Vice are more like Archetypes which you choose from a list. They provide some game-mechanical effects for when you recover Willpower.
Distinct vs. Unified Attack/Damage Rolls
In Storyteller, you roll to hit, the enemy rolls to dodge/parry/block, then if you hit you roll damage and the enemy rolls soak.
In Storytelling, the attack/damage roll is a unified thing, and the unified defence value is subtracted from the attack; attacks are resolved in a single roll; this means that weapon value de facto improves your chance to hit, but usually doesn't guarantee a minimum damage.
Humanity for Vampires vs. Morality for Everyone#
In Storyteller, Humanity is largely a VtM thing, not something applied across the system.
In Storytelling, all mortals start out with a morality mechanic, but it can be adjusted for different splats (e.g. the specific sins may be different between mortals and splats; names may also change).
In Storyteller, Flaws give you Freebies immediately, and 'stay on', complicating the character's life when relevant (e.g. bad sight making vision-related perception rolls and some other rolls harder).
In Storytelling, Flaws don't normally grant any points immediately, but when a flaw complicates a character's life, that character's player receives an experience reward (with a limit on frequency).
Representation of Speed in Combat
Not something specific to any one splat, but while in Storyteller, characters who are significantly faster than others in fluff are also significantly faster in crunch, i.e. someone who's twice as fast as a normal human (whether due to time-warping, vampiric speed or whatever) acts that many times more often. In Storytelling, such representation is avoided.
A Word on Compatibility and Portability
The two systems are significantly more different than than the differences between any two of the pre-anniversary editions of World of Darkness Storyteller system variants. I would say that Storyteller and Storytelling are approximately as different as (pre-anniversary) Storyteller and Exalted 2e. A character made for one would not be playable in another without a lengthy conversion.
That being said, individual subsystems are at times close enough to enable portability - using a subsystem from one with minimal adjustments to use with the other. For example, it's possible to replace Nature and Demeanour with Virtues and Vices, or vice versa, and retain a playable system, and even be able to use many (most? all?) abilities intended for one with the other. Similarly, I've heard of people who use Mage the Awakening magick game mechanics to run a Mage the Ascension campaign, and say that the net effect from the change was an improvement. The portability of individual subsystem varies however - e.g. combat is so radically different that porting over mechanics from one system to another is likely to either break a lot of stuff, or require a lot of adjustments.