Your question seems to revolve around the probability that two things are different, not the degree to which they are different. Using basically refers to the degree they are different.
A quick look at dictionary definitions shows that probably is synonymous with most likely, however from usage, why would the phrase most probably then exist?
likely to be different
means a greater than a 50% chance
most likely to be different
means something much greater than 50%, for example 90%
are different
definitely different
inherently different
completely different
totally different
implies they are different with certainty (probability of 1.0)
To me, most likely has a greater chance of being different than just probably, whereas likely and probably are equivalent. However, in your example, most likely still leaves the door open that they may be different, which makes phrasing difficult since the degree can always be modified by more or very which would make it two words, not one word.
I don't believe we have a single English word for it. There is a term, but it isn't widely known.
It is called dimorphous expression, or "cute aggression" by psychologists and defined as "superficially aggressive behaviour caused by seeing something cute, such as a human baby or young animal". It is not real "aggression", but a primal feeling you want to squeeze them harder than you should, or perhaps bite them.
Wikipedia says of this behaviour:
"People experiencing cute aggression may grit their teeth, clench their fists, or feel the urge to pinch and squeeze something they consider cute, while not actually causing or intending to cause any harm."
I have never heard these terms used in everyday speech. If you were to use the term you would likely have to explain it. Most people would just express how they were feeling by description, perhaps using adjectives or superlatives.
A very commonly used expression is:
He/she is so cute I could just eat them up!
Best Answer
You might call it a stifled laugh, as in, “Mary tried to contain herself, but couldn’t help letting out a stifled laugh.” You could also use the word snicker (either as a verb or noun) or possibly titter - though the latter might sound a little dated and silly.