The 70-300 will give you greatest magnification compared to a 'standard' lens though it may not necessarily focus as close as the 18-180mm.

I think the confusion you feel is down to marketing phrases such as 10x zoom which truly refer to the ratio of the longest focal length to the shortest. By this method the 18-180 comes out as a 10x zoom while the 70-300 is 'only' a 4.2x..... but, and it's a big BUT, 300mm is still 1.7x longer than 180mm. The net result is that at 300mm the 70-300 will give you an image almost 17x bigger than an 18mm setting...

Once upon a time in the days of film this sort of magnification comparison was based on a 50mm standard lens. With the Oly system this 'standard' lens is roughly 25mm. Based on this the 18-180 would allow you a maximum magnification of 7x standard while the 300mm comes out at 12x.

Any way you look at it the 300mm makes things look much closer then the 180...