A checkpoint contains the value of (some of the) variables in a TensorFlow model. It is created by a Saver, which is either given specific Variables to save, or by default saves all (non-local) Variables.
To use a checkpoint, you need to have a compatible TensorFlow Graph, whose Variables have the same names as the Variables in the checkpoint. (If you don’t have a compatible Graph, you can still load the values stored in a checkpoint into selected Variables using the init_from_checkpoint utilities in contrib.)
SavedModel is much more comprehensive: It contains a set of Graphs (MetaGraphs, in fact, saving collections and such), as well as a checkpoint which is supposed to be compatible with these Graphs, and any asset files that are needed to run the model (e.g. Vocabulary files). For each MetaGraph it contains, it also stores a set of signatures. Signatures define (named) input and output tensors.
This means that given only a SavedModel, you can write tools (such as tensorflow/serving, or the new saved_model command line utility that will appear in tools/ shortly) that interpret or execute the graphs inside. All you have to provide is the data.
If in doubt, I would always err on the side of writing a SavedModel, not just a checkpoint. Not only does this allow you to use tensorflow/serving (and other neat utilities that will grow in number), it makes sure that you have all the information necessary to run the model. Nothing is more frustrating than a checkpoint you cannot use any more because you modified your model and now it is incompatible with checkpoint files and all you want to do is run some predictions through it for comparison.