You can specify which is which by saying maternal grandparents (your mother's parents) or paternal grandparents (your father's grandparents). I know of no single word in English that makes the distinction.
Some families get around this ambiguity by referring to both sets of grandparents with different terms of affection (for example, the mother's mother might be "Nanny", while the father's mother might be "Grandma", so, when one parent says, "We'll be going to Grandma's for Christmas," the children know where they are going).
I should note that the terms maternal and paternal are seldom used. For example, in your sentence, I would simply say:
"I visited my grandmother today in the hospital."
Sometimes, though, maternal and paternal can be used for clarification:
"After the fire, Emily went to live with her grandparents for awhile, while her parents recovered in the hospital."
"Which grandparents?"
"Her maternal grandparents."
although the speaker is probably just as likely to respond with:
"Her mom's parents."
One other way this is often communicated in English is by using the phrase "on my mother's side" (or "father's side"). So, in the conversation about Emily, one might hear:
"Her grandparents on her mother's side."
Or, to use your original example:
"Today in the hospital, I visited my grandmother on my mother's side."
Credit and thanks to mcalex for mentioning on my mother's/father's side.
Best Answer
There are many languages that differentiate relatives much more than English does. So you can have different words for aunts, uncles, grandmothers, and grandfathers on your mother's side and your father's side. I suspect your native language is one of these.
English doesn't do this. The distinction isn't important enough to require separate words for each. We usually don't bother specifying the relationship any further, and when we do we add the words "maternal" (formal) for our mothers' side and "paternal" (formal) for our fathers' side before the word for the relative. Informally, we just say "uncle/aunt on my mum's/dad's side". However, this doesn't completely define the relationship for aunts and uncles. If I say "paternal aunt" it's either my father's sister, or my father's brother's wife (my father's sister-in-law). (Note that my father's sister-in-law can also mean his wife's sister, who is not related to me if my father's wife is not my mother.)
Some languages also have terms for older brother, younger brother, older sister, younger sister, etc. Using these words shows respect by acknowledging a hierarchy within a family. Not only does English not have the equivalent words, we also have a word "sibling" which is either a brother or a sister without specifying the gender. Many languages don't have a word for "sibling", e.g. instead of asking "Do you have any siblings?" you have to ask "Do you have any brothers or sisters?"
So, in English we have different words depending on the gender of the relative, but not different words for exactly how they're related. Many of our terms are ambiguous without going into more detail. We also have non-gender-specific words for most relations: parent, child, sibling, grandparent, grandchild, cousin. We don't have non-gender-specific words for aunt, uncle, niece, or nephew.
The many comments this answer has attracted shows how the words mean just what they mean, no more, no less. An aunt can be on your mother's side or your father's side. She could be related to you by blood (one of your parents' siblings) or she could be related to you by marriage (one of your uncles' wives). English doesn't specify any further than that, and usually it's not important enough to clarify the situation.
Your language might not have words for "one parent's brother" or "one parent's sister". A native English person learning your language might find this strange but they would cope after a while. Not having more specific words than "aunt" or "uncle" might seem strange to you, but it's the norm in English to not be more specific. Our language is influenced by our culture and our culture is influenced by our language. Apparently, there is no cultural or linguistic need in English for more specific words.
Both of my parents are only children, so I have no natural aunts or uncles. Everyone I call "Aunt" or "Uncle" is actually a great-aunt or great-uncle (my grandparents' siblings), or a cousin of an appropriate age (i.e. roughly my parents' age).
Something about different languages is that although they can all express the same ideas, often there are no direct translations. This is one of those cases. The most natural way is to just say "aunt" or "uncle". Only specify it further if it's important to do so.