In this question, the accepted answer says that a visit is not always an entrance. I checked and it's true for my site, though the difference is small (0.4% difference).
difference between ga:entranceBounceRate and ga:visitBounceRate
When is a visit not an entrance?
Visits are incremented with the first hit of a session, whereas Entrances are incremented with the first Pageview hit of a session. So if the first hit of the visit is not a Pageview then you might see a difference between these two calculations.
ga:entranceBounceRate = (ga:bounces / ga:entrances) * 100
ga:visitBounceRate = (ga:bounces / ga:visits) * 100
For example:
So to sum the example up you'd have 3 visits and 2 entrances which would yield different results for those two calculations.