When viewing coverage from BAM files at base level total count is the total number of alignments that cover that base. Downsampling does not apply here, reads are counted prior to downsampling.
The signal from a TDF file should correlate, but there can be differences particualrly if you have clicked "normalize coverage". TDF files use bins (windows), by default 25 bp in width. The lowest resolution signal in a TDF file is the average count over the window. As you zoom out these windows are combined to give a signal at the resolution you are viewing, that is the base pair width corresponding to a pixel. If "mean" is used as the window function (the default), this will normally flatten peaks.
If normalize coverage is checked the signal in a TDF file, as described above, is multiplied by (1e6 / total # of alignments), where total # of alignments is the total # of mapped reads in the bam file. The purpose of this transform is to compare bam files whose total coverage might differ. This is a very crude normalization obviously. The normalize coverage option has no effect on the total count value computed directly from the bam file.