I suddenly thought about these 2 compounds that seem to have the same name. Aren't both of them methyl propanoate? How do we differentiate them apart name wise?
From context (in spoken word) and/or the presence or absence of a space (in written word). The one on the left is a neutral molecule whereas the one on the right is a charged molecule. In mentioning the given compounds there should be context to indicate a charge. For example, the one on the left is "methyl propanoate", whereas the one on the left would be "2-methylpropanoate" (also called isobutyrate). The isobutyrate would usually be described as an ion (e.g. "sodium methylpropanoate") which would provide clarity as well.
Now it is possible to see the 2-methylpropanoate written as just "methylpropanoate" since there are no isomers to cause ambiguity. In either case, though notice that names for the left molecule have a space between "methyl" and "propanoate" whereas names for the right molecule do not. That is how you can tell between an ester from an anion.
There is not supposed to be a space between the substituent prefixes (e.g. methyl) and the parent structure (e.g. propanoate), so your second structure is methylpropanoate, or more correctly 2-methylpropanoate.
In the ester there is a space between methyl and propanoate, i.e. methyl propanoate.