Yes, a huge difference.
Thinner is a universal term, just like solvent. Water is a solvent, water is a thinner, but water won't thin enamel.
To successfully work with paint, you need to use either what the base is or a very similar product.
Perfect example is Tamiya acrylics. They're are actually ether based, that's why they are flammable (how many acrylic paints can blow up?) and high concentrate alcohol works well with them.
Windex, which is ammonia works with others.
Thinner at a hardware store may be acetone, turpentine, denatured alcohol, etc.
Beware of the big cheap containers, you're not necessarily coming out ahead. MEK is active ingredient in Tamiya Thin, Tenax, PlastiWeld and will melt styrene or ABS like a champ, but the jug of MEK substitute at the hardware store doesn't bond anything.