- My house is the tallest in my town.
- My house is tallest in my town.
Are these two sentences the same or different in meaning?
The sentence without the means the same as the sentence with the.
Tallest, with or without the means (the) most tall. It does not mean very tall (something you suggest in a comment).
Note that it is customary to use the definite article with the superlative in most contexts. However, there is no rule that says one has to. In addition, there are some constructions or concatenations where it is usually not used.
For example, in the sentence:
Fastest land animal in the world: the cheetah can reach speeds of...
Also:
My cherry pie won best-in-show.
See the link provided by Araucaria to see other examples of a superlative (fastest) used without the.
Please note that this is a a rule of thumb and may not always fit.
The superlative with "the": this means it is the most [adjective] out of all relevant objects, with whatever limitations are applied. It is like (re)stating the object after the superlative.
My house is the tallest in the town.
My house is the tallest house in the town.
The tallest house in the town is my house.
This is the more common than without the "the".
The superlative without "the": this means it is true for the specified object compared to itself when all of the restrictions apply. It is like adding a "when" after the superlative.
My house is tallest in the town.
My house is tallest when in the town.
When in the town, my house is taller than at any other times.
This doesn't make sense for all objects or scenarios, like a house since they do not move. An example that makes sense:
I am happiest at home.
I am happiest when at home.
I am happiest when I'm at home
An example where these rules don't work:
Which season is coldest? (This is obviously comparing all of the seasons but lacks a "the".)
The superlative always uses 'the'. Your sentence 2) just isn't standard English, however you came to learn it.