A lead sheet is the bare bones of a song. The top piece is a lead sheet. It is made up from the single notes providing the melody, while the l.h. part is just not there. That's due to the chords being written out as the song progresses, for a chordal instrument (usually piano or guitar) to provide the backing. That could be played as full chords, dyads/triads, on piano, or provide enough information for a bassline on bass or l.h. piano, the player may then use the r.h. for chords. Obviously if there was a singer, they would use the top line, leaving the accompanist to play whatever else fits.
The other is not a lead sheet. Notice it has 3 lines in parts. That's to differentiate the vox from the two-handed piano part. It's a specialised arrangement which could be played just on piano, but there's 'bass' written in for a bass guitar rather than l.h. piano to play - they could even double. Thee 3 staves is a very common way to write out songs, and is usually standalone, whereas lead sheets are more of a guide - for players who may put more or less into the performance.