Changing the extension in a file name by typing in another will NOT change the file format OF the file. You should never do this anyway.
An EPS file of your logo can be imported into other design software. It is unlimited resolution and can be enlarged without image degradation. Can be edited (with appropriate software & technical knowledge) and used as a source file for other file types. Primarily a print file and NOT for use on web. You can make bitmap or pixel images from a vector file, but usually not vice versa.
JPG files are primarily for use on monitors and TVs. Used extensively on most web based platforms and applications. Can be compressed to lower file size (and speed up download over the internet) but some image degradation may be apparent. Cannot be used larger than 100% of original image size. ALWAYS features a background color. Difficult to edit.
PNG format can feature a transparent (clear) background. Great color accuracy (though blends or gradients may “band” with lower bit rate files.) Cannot be used larger than 100% of original image size though reduces well. Considered universal standard for pristine logo presentation on websites and electronic media, though not fully supported by some platforms (those that don’t usually convert PNGs to JPGs.) Difficult to edit.
JPEG (or JPG) – Joint Photographic Experts Group
PNG – Portable Network Graphics
GIF – Graphics Interchange Format
TIFF – Tagged Image File
PSD – Photoshop Document
PDF – Portable Document Format
EPS – Encapsulated Postscript
AI – Adobe Illustrator Document
INDD – Adobe Indesign Document
RAW – Raw Image Formats