The old Amazon Alexa App was our very early method of providing some Alexa functionality. It only supported dimmers and switches by emulating a Hue Bridge. There were many shortcomings to this approach.
The Amazon Alexa Skill is our new and improved app, involving the installation of a skill via the Alexa smartphone (or web) app. This has much improved functionality, and supports a broader range of devices. This will be our main integration going forward.
When we first introduced the Alexa Skill, there were problems getting it to work in the UK. We have been attempting to correct this. Yesterday we pushed out a build that actually broke the skill installation, and did not help the UK problem. We plan to release a hot fix today to correct that bug. We brought back the old app to allow the UK users to continue to have Alexa functionality while we resolve the issues in the UK.
You can only have one or the other installed. You cannot install the Skill if the old app is installed. It needs to be removed before you install the skill. Were you to install both, it would mess up Alexa's device discovery and would probably not work at all for either app.