Difference between histogram and bar chart?

A histogram is one kind of bar chart.

Bar charts

If we want to represent the data collected about qualitative variable then a bar chart is the simplest method to employ.

The gaps between the categories in a bar chart are important: they emphasise the fact the categories used are mutually exclusive and do not form a continuum.

Histograms

Like bar charts, a histogram is produced by sorting data into categories (called bins). However, unlike a bar chart, the values on the x-axis form a continuum: the point at which one bin ends is the point at which the next bin begins. For this reason, neighbouring bars in a histogram must touch. In a bar chart, frequency is expressed as the height of the bar; whereas in a histogram it is expressed as the area of the bar.

Unlike a bar chart, where the gaps between the bars stress the absence of a continuum on the x-axis, the gaps in a histogram have a different meaning. Because the x-axis is a continuum, a gap in the data indicates that there were no data values in this bin.

The shape of the histogram depends on the choice of x₀ and the bin-width, and making the wrong choice can led to flawed interpretations. Too many bins and you cannot see the structure of the data properly due to the presence of too much information; too few bins and you cannot see the structure at all. There are various methods for choosing the ideal bin-width, but none is definitive.

Also, Both are used differently.