What connection does the Jesus movement and the pentecostal/charismatic movement have, if any?

Background:

Firstly, the advent of Pentecostalism significntly preceded both the Charismatic Renewal and the rise of the Jesus Movement - the former arose out of the Holiness movements of the late 19th century and really kicked into gear with the Asuza street and Welsh revivals of the early 20th century, while the latter two, although heavily influenced by the former, were '60s children' (Charismatic renewal starting in early 60s, Jesus movement taking off in the late 60s).

The wikipedia article on the Jesus movement is both a little confused, and a little confusing, this is most likely because that description is true of the movement itself - it was diverse and quite spontaneous in it's rapid and widespread growth from multiple 'ignition points' and what influenced it and what came from it is an extremely tangled network. You can get a good sense of the times from reading Keith Green's autobiography "No Compromise"; brief histories here and here; or the following Charisma magazine article from Larry Tomczak here*; and I personally had my interest piqued in those times by hearing first hand accounts from Winkie Pratney who was a leader in the movement and familiar with many of the key players.

Seminal moments and locations were the opening of 'the Living room' - an evangelical street mission in San Francisco's Haight-Ashbury district (1967); Arthur Blessit's street ministry on Sunset Strip (West Hollywood) (1968); Jack Spark's campus ministry at UC Berkeley; and Linda Meissner's ministry to youth in Seattle.

Contrary to what the Wikipedia article implies, the Calvary Chapel was not a 'product' of the movement, but existed before (founded 1965), and was a key player in fostering the movement on the West Coast of the U.S.A. (starting from 1969). Although the movement was national and ultimately international in its reach, the West Coast of the U.S.A. was probably the 'ground zero' of impact, and the Calvary Chapel movement was both considerably benefited and challenged by the rapid influx of new believers that came as a result of the separate yet relationally linked Jesus movement. What it does get right however, and this is most pertinent to your question, is the strong pentecostal/charismatic 'flavor' of the movement. It's possible there were pockets of the movement that didn't pursue and experience the sign gifts of the Holy Spirit (for instance, arguably the 1970 Asbury Revival in Wilmore, Kentucky, although links to the wider Jesus Movement are obscure), but they were few and far between. Chuck Smith (pastor of Calvary Chapel) started out as a pastor for the International Church of the Foursquare (Pentecostal) and under his direction, the Calvary Chapel movement, while backing away from Pentecostalism as a defining characteristic, remained (and continues to be) strongly Charismatic (Evangelical) in character. One of the key leaders in the Jesus Movement was 'power-evangelist' Lonnie Frisbee - a disciple of Chuck Smith and a highly influential and controversial figure in the Jesus Movement. There is no doubt that controversies surrounding Frisbee and others like him in the movement (bearing an uncanny resemblence to the early Corinthian believers as they came out of a sub-culture that more closely resembled that of early Corinth than the 'square' culture of mainstream America) likely resulted in the movements gradual dissipation from the early to mid '70s through to the mid '80s. As well as the Calvary Chapel movement, The Vineyard movement, Maranatha Campus Ministries, Contemporary Christian music and many other ministries were impacted by the legacy of the Jesus Movement - a large (if not overwhelming) majority of them being Pentecostal or Charismatic in nature.

To provide a generalised summary answer to the first aspect of your question:

What connection does the Jesus movement and the Pentecostal/charismatic movement have, if any?

To a significant degree, the Jesus movement arose from earlier Pentecostal influences (e.g. Blessit, Meissner, Smith were all from Pentecostal backgrounds), Concurrent with (or slightly after) the wider Charismatic renewal (It is legitimate to see the Jesus Movement embedded within the context of the Charismatic Renewal). It's effects contributed to the origin, diversity and vitality of many Pentecostal, but particularly (non-denominational or new denominational) Charismatic churches and ministries.

In regard to the last aspect of your question:

Have people in the Jesus movement influenced the Pentecostal/charismatic movement in any way, like joining some Pentecostal/charismatic church after the Jesus movement ended?

Yes, absolutely - Dr. Michael Brown (later associated with the Brownsville revival) is a notable example of exactly this, and he is by no means alone - various influential leaders and people associated with the movement that went on to have impact through subsequent ministries can be found here.

Further resources: here and God's Forever Family: The Jesus People Movement in America, Larry Eskridge - excellently reviewed here.

*The Jesus Movement is a not uncommon theme in Charisma magazine articles