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
I've found a saying that seems to be related to the meaning described by you:
Live and learn (Wiktionary): An exhortation to gain knowledge from living experiences. Commonly used after an accident or misfortune to indicate a moral lesson.
It is also mentioned as
You live and learn (The Free Dictionary): something that you say when you have just discovered something that you did not know.
There's a sample sentence:
P.S. In Russian, we have a saying "Live for a century and learn century through" (Век живи, век учись - Vek zhivi, vek uchis'). Or, "one lives through one's life and learns all through one's life", since the word век has an antique sense of 'human lifespan'. It is used to be said exactly in the manner of "live and learn", after one has discovered something previously unknown. Sometimes the contemplative ending ".. and still one dies a fool" is added.