You use “pero” when you mean “but”.
“Medyo” is from the Spanish “medio”, which means medium or midway. In Tagalog, it does not mean a mid-point though, but instead, a more general “less-than value” to the word it is being used to modify. Hence, it can mean “kind of”, “a bit”, or “somewhat”. Filipinos often use this word to soften a negative description of something so as not to sound condemning or confrontational or too offensive. We also use it when we are uncertain about how to describe something, especially if the thing is supposedly measurable. It may also be used to produce a humorous effect in some situations.
“Masarap yung niluto mo kaya lang medyo maalat”. = The food you cooked is delicious, however, it’s a bit salty.
“Medyo tinanghali ako ng gising” = I woke up kind of late.
In these 2 examples, we know that salty is salty and late is late, but by adding “medyo”, we try to reduce the intensity of the descriptions. We, therefore, try not to offend the cook in the first one, and try not to forgive ourselves for oversleeping.
Uncertainty (the same effect when we use “kind of” in English):
“Ang girlfriend ni Paul ay medyo matangkad”. = Paul’s girlfriend is a bit tall. (Here the speaker knows that the girl is taller than normal, but not that tall, and neither does he know exactly how tall).
Guy: “Mayaman ba kayo?” = Is your family rich?
Girl: “Medyo lang.” = Just somewhat (rich).
(Guy asks a foolish question, he gets a foolish answer.)
You may also use “pero” and “medyo” together. The first example above may also be stated as:
“Masarap yung niluto mo, pero medyo maalat”. = The food you cooked is delicious, but a bit salty.