TL;DR: Those not curious about marketing and technical details can skip this.
There may be a variety of things going on when you see 2 similar interfaces, some of which you have mentioned. Here are a couple of additional possibilities:
1) In the process of developing code, there are code modules available these days that you can just plug in to your development framework. That way, a developer does not have to rewrite commonly-used internal functions and external user interfaces. It’s possible that Taskrabbit and Airbnb are using some of the same publicly-available libraries.
2) When vast amounts of users use a particular product, the product’s interface can often become a defacto standard. Some software shops will adapt some of the interface behaviors of their product to resemble a wildly popular one, for a few reasons: a) to sell ease of use, as customers are already familiar with it, and/or b) for marketing purposes, since people are drawn to that which is familiar to them. This is where patents and copyrights come into play, to protect against another entity capitalizing on a company’s popular ideas and designs.
It could also be as you mentioned: the 2 companies are in some sort of strategic partnership, with a future goal of Airbnb taking over Taskrabbit.