In your first example 'also' could be used in response to someone else, presumably your girfliend or wife, saying that she knows the difference between your love and hers. (1)
It could well be used to mean something like that: I know the difference between X. I also know the difference between..... (2)
Also as used in your second sentence simply introduces a new thought. (3)
I don't know whether #3 is grammatical or not. If it is is, I'd say it means (1).
There is little marked difference in essential meaning, but there are subtle differences of nuance and ephasis, and as with much else in English, these will tend to be contextually determined.
(a) I also know the difference between my love and yours.
(b) Also, I know the difference ..
(c) I know also the difference ..
(a) and more rarely (c) would usually be said when the speaker has claimed in the previous sentence to know something else ("I know that you are under great pressure at the moment. I also know..."), or where the interlocutor has done so ("'Your love and mine are different in this respect', she said. He replied: 'I also know the difference...'") - here it is virtually the same as "I too know the difference...";
(b) would be tantamount to "moreover" or "furthermore", and would be said when the speaker has made some other claim ("You are under great pressure at the moment. Also, I know...").
(c) is, incidentally, not ungrammatical, it just feels a little odd, but that is in the cold light of a contextless discourse. As often, in actual conversation the vocal stresses will contribute subtly to the intended sense.