Samba is a Brazilian musical style. Originating from folk traditions, it grew at the beginning of the 20th century and blossomed into lots of sub-genres. This recording is from 1916 and includes a repeating rhythm in the accompaniment (notated below). The syncopation of it is what characterises it as samba.
The second video is of a televised performance from 1967. "Mas Que Nada" is a well-known song which incorporates quite a slow and disjunct melody with a very active and energetic accompaniment.
Batucada is a highly percussive style of samba characterised by syncopation and a fast tempo. It is the type of samba people are most used to hearing at carnivals, festivals and other outdoor events.
As this video shows, it is often led by someone who cues section changes and who might do call and response with the other musicians. The music is highly energetic and vibrant.
The music of samba has more recently been fused with EDM styles to modernise the style and create something which is catchy, exciting and patriotic. The triplets at 0'30 in "Samba Do Brasil" are an additional rhythmic feature which support this really effectively.