It is called Apache Cordova now, and it is a set of implementations (one for each platform) providing JS hooks into native APIs, so they can be called from JS in a web view, so your web app runs in a native app container.
Phone gap is now a set of technical/busisness services for managing Cordova projects, such as Build deployable packages for all platforms via a web service
PhoneGap is getting better with every release, and it isn't too hard to make a nice, functional app. The promise of cross-platform holds only for so long - until either a plugin doesn't exist for the platform or a platform-specific glitch gets in the way, but overall it is a fun and rewarding thing to work with.
Clients want apps in stores. It's much easier to promote than mobile web apps. And even though for a nicely looking, nicely working cross platform phonegap app you will be paying a lot of money (the tweaking takes a lot of time between different phones/pads), it is still cheaper and faster than going native.
We advise native for productivity apps and such; day to day use apps should be fast and snappy, while promotional apps / marketing apps should look pretty.
It sounds like you make apps for people. Assuming you have someone on staff who knows iOS and someone who knows Android is it still faster to do it in PhoneGap? We attempted a phonegap app which ended up failing because of performance reasons. We rewrote the app in native iOS and it didn't take nearly as long as the original phonegap did with the constant tweaking in an attempt to get it to look and perform acceptably.
It depends definitely on the app; we have been in the 2 camps. The problem is that often we are also asked to make the mobile web site and then you have 3 very similar things in Phonegap while native you need to write 3 different things. I do agree though that for a lot of apps native is faster to write if you target one platform.
And the Phonegap experience isn't really good unless you spend a huge amount of time. Webview is just not very good; you need something which is native but crossplatform to replace it; everything we tried so far (appmobi, appcelerator, rhomobile) actually was worse than Phonegap/jqm to get right. But we keep at it as we know what our clients want.
Often the Phonegap version is treated like a prototype; then the client saw it and knows what they want; after that they have it rewritten to native on the platform which makes them the most/gets the most attention (etc). Which is almost always iOS by the way.
My current client is using PhoneGap to enable publishing to numerous device types without the need to hire developers for each platform. Particularly important due to their customers' global spread; supporting multiple platforms is a decided competitive advantage and finding devs is tough these days.
Unless it's changed a lot since 1.0 I don't believe it's some kind of WYSIWIG iPhone maker that creates bloated, terrible, code.