You're Correct!
There are many different looking putter heads on the market today, but they are generally put into one of two categories - the blade headed or mallet headed.
To look at these different shapes you would see that there is a big difference visually, but that does not mean that the performance of the putter, which is the ultimate goal, is different from one shape to the next.
If you pick up two blade style putters off the shelf in your local pro shop and rest them both across the palm of your hand, you will see that one putter face will stay closer to the horizontal and the other one will hang down more towards the vertical. This is due to the amount of weight that has been distributed between the heel and the toe of the putter. The putter that hangs down more towards the vertical has more weight in the toe end. This will see the putter want to work on more of an arc during the putting stroke, likewise the putter that hangs closer to the horizontal requires less arc in the putting stroke. If your stroke has a small amount of arc in it but the putter your are using is weighted more to the toe, then your missed putts will be dispersed wider around the hole as the putter being used does not fit your stroke.
You can do exactly the same test with two mallet headed putters, and although you may have to pick up a few different putters at first, you will also find that the majority of mallet style putters will sit closer to the horizontal, but there are some that will hang closer to the vertical.
No matter what the look or style of the putter head is, the most important part in making your choice is to check that the putter head is weighted to fit the arc of your stroke. Next time you are buying a new putter, remember this - the way in which the manufacturers position the weight within the putter head has the biggest effect on its performance. If you know the type of putting stroke you have then you can fit the perfectly weighted putter to your stroke type for the best possible results.
Sorry Try Again! - See Explanation Below
The difference between a blade and a mallet headed putter is easy to see. The blade head is so named due to its long face but thin width design with a very slight alignment aid on the top, whereas the mallet head is traditionally more of a semi-circle in shape with a slightly smaller face but it is much wider and provides you with a larger alignment aid on the top.
Sorry Try Again! - See Explanation Below
No matter what the design of your putter head the way it sits on the ground will be determined by two things, the lie angle of the putter where the shaft comes out of the head and the length of the shaft. If either one of these are incorrect for you then your putter will not sit on the ground correctly.
Sorry Try Again! - See Explanation Below
The position of the weight in the putter head is designed to help the type of stroke you have. The more the weight that is in the toe end of the putter, the more arc you will need to have in your stroke for you to be consistent. Likewise, the more the weight is spread out across the face of the putter, the less arc you will need in your stroke.