Video is measured in terms of vertical resolution, so 1080p = 1920x1080. 720p = 1280x720. PAL = 576i, being 720x576. NTSC = 480i, being 720x480.
Digital Cinema (digitized film, or digi-cine cameras) have their formats represented in "K", which is shorthand for the horizontal resolution. So a frame that's 2048 x 1152 = "2K", since "K" is shorthand for 1,024 (or, sometimes, rounded off to 1,000).
Digital cinema scans are usually done at 4K (4,096 x 2304) or 2K (2048 x 1152).
Still photography usually doesn't use either nomenclature, they instead just refer to the total megapixels. So a 4096 x 3072 sensor would be called a 12MP sensor (since 4096x3072 = 12,582,912, rounded down to "12 megapixels"). And so stills shot at that size would be 12-mp stills.
So -- let's go back to the GH1 -- as a video camera, it's a 1080p camera. It records actual video files, at 1920x1080, hence 1080p.
As a still camera, it's a 14-megapixel camera.
And in terms of its sensor, if it were to be classified as a digi-cine sensor, it'd be about 4.3k (since its raw sensor resolution is something like 4352 x 3000).