What is the difference between AEO and VO bid types on Facebook?

What @ESeufert said in his answer. I'd underscore this additional point about VO:

The impact of VO optimization is significantly stronger if you use value-based lookalikes(based on a customer list with revenue numbers, or based on monetization data being passed back to the FB SDK).

This strengthens Facebook's feedback loop because the algorithm sees which users have already spent more money, and which ones have spent less money; and it attempts to show more ads to users resembling heavy spenders - and fewer ads to users resembling low spenders.

AEO standards for App Event Optimization and VO stands for Value Optimization. The easy answer to this question is that these two different campaign types optimize on different things: AEO targets people whom FB's algorithm presumes will complete some certain event, and VO targets people whom FB's algorithm presumes will spend some amount of money within a certain amount of time (expressed to Facebook as a percentage of spend, or recoup).

The long answer is that AEO will look for people that Facebook identifies as being similar to those that have completed some pre-identified event in your app. Let's say that you are running an AEO campaign in Facebook and you have used the "Complete Tutorial" event as your optimization point. Facebook will start sending you traffic for the campaign and observe which people actually get to the Complete Tutorial event (they'll know this because you send them a signal when a tutorial is completed). Facebook then tries to parse out commonalities -- shared traits -- amongst the people that have completed the event, and they change the campaign's targeting to expose your ads to more people like that. With AEO, you can specify a target Cost Per Event (CPE) bid value, or average cost you are willing to pay for a user that completes that event, and Facebook uses that target in serving ads to more people. With respect to recoup, the responsibility is the advertiser's to decide how the optimization events being used by the campaign correlate to revenue and ROAS (ie. people that complete tutorials may not be likely to actually spend money).

VO campaigns are a little more byzantine as they rely more heavily on the proprietary data that Facebook has on its users and, frankly, there is less of a precedent of the VO type from other large advertising platforms. Facebook's explanation here puts forth that VO campaigns simply impact targeting: Facebook uses early monetization feedback from cohorts to do the commonality identification (as noted above) to find users that look like the ones that have spent a lot of money, and it sets the threshold for that based on the ROAS target that the advertiser specifies in campaign creation (eg. if I say I want 10% Day 1 ROAS, it'll target higher-spending users than if I say that I want 5% ROAS). You cannot specify a target bid for VO campaigns (as of this writing), only a target ROAS goal.

What Facebook hasn't made public is whether it only uses monetization data from an advertiser's campaigns in targeting users or if it has a broader, user-level monetization likelihood feature that it uses to find users that are likely to spend in any product. If monetization likelihood at the user level (versus the campaign level) is used -- and Facebook hasn't indicated publicly whether it is or not -- then it'd speed up the campaign learning process by seeding the campaign with better prospects, although products would need to be clustered in order for that metric to be relevant (eg. a user that monetizes in free-to-play mobile games might not necessarily be a relevant, likely monetizing user for a travel app).