is there any difference between them paying for a relocation vs giving
me roughly the same amount as a sign-on bonus?
Often these are budgeted differently, so that is one difference from a company point of view.
Some companies standard practices grant one of these costs and not another. For example, my company sometimes pays relocation expenses. As far as I can tell, they never pay sign-on bonuses.
From your point of view, I think one-time money is just money.
As @Ida correctly points out, some companies (particularly large companies) offer relocation assistance on a regular basis - sometimes to the point of having a contracted rate for those services. In that case, it's not money - just the service - that you receive.
If you don't know the company's standard practices in this area, you could always ask for both. (It seldom hurts to ask.)
How far you want to press the issues is very context-dependent. You may be in a very high-demand industry, or may individually be a very desirable candidate - someone at whom companies will throw money.