Yes. In the beginning they would actually sit down and sing into each other's face while they wrote a song together. They once went off into the corner of a bar and in about an hour wrote 'I Wanna Be Your Man' for another patron at the bar that night, Mick Jagger. As time went on, it got to be more of a thing where one of them would come up with a stanza and the other would write the "middle 8". For example, 'We Can Work It Out' was a McCartney song where Lennon wrote the, "Life is very short, and there's no time... for fussing and fighting my friend", middle 8. (Any line with "my friend" in it was a Lennon line.)
It also got increasingly easy to tell who wrote what by virtue of who sang the song. The writer was usually lead singer on his own song, but not always. For example, Lennon's harder rock voice is more prominent in McCartney's 'Eight Days A Week'. (I think George Martin figured that one out.) And as with 'Getting Better', the Lennon stuff had an "edge" to it that was easy to pick up. Violence, drugs and the surreal were more down Lennon's alley, while McCartney tended toward the pop and sentimental side. (Although McCartney liked the occasional pot reference, and could have an "edge" of his own at times.)
Maybe the best example of the differences between the two great composers was evidenced by what they vetoed. When McCartney came up with 'World Without Love', Lennon laughed and made fun of the "Please lock me away" line and they ended up giving the song to Peter and Gordon instead of recording it themselves. Likewise, when John came to Paul with 'Cold Turkey', which he wanted to release as a Beatles song, McCartney basically told him, "No way, are you NUTS!?! So Lennon recorded and released it on his own (with the Plastic Ono Band, if I recall correctly).