2 very different things imo. One is clear instances of racism. If a cake shop is objecting to making an LGBT wedding cake on religious grounds, I don't think it is right to force them to make the cake, that violates the owner's religious rights. The same goes with trying to force a conservative Christian pastor or priest to be the officiator at an LGBT wedding.
The bible pretty clearly speaks against LGBT stuff in several places (Leviticus 18:22, Leviticus 20:13, Romans 1:25-28, 1 Corinthians 6:9-10, 1 Timothy 1:10, Deuteronomy 22:5, among others), so many Christians just don't feel comfortable having any degree of participation in an LGBT wedding. Believe it or not, most Christians don't have hate in their hearts for LGBT people, we love all people just as God commanded us to and many Christian churches have no issue with LGBT people attending, but at the same time we can't really deny what the Bible says about LGBT stuff; if it is a sin as it seems to be, we ourselves would be participating in sin if we took any part in an LGBT wedding. As a Christian myself, I'm not against LGBT marriage, if they want to do it and risk sinning, that is between them and God in my eyes, none of my business. I just wouldn't feel comfortable participating in an LGBT wedding myself, as anything more than a simple guest maybe. I also have no issues with being friends with LGBT people, and have several LGBT friends and acquaintances.
Didn't answer the question. They are not different things at all, they are the exact same thing. Refusing to sell a cake based on beliefs. The only potential difference is that one person claims their beliefs are religious, but perhaps they are lying, or perhaps the other person also cites religious beliefs.
If you don't want to bake a cake for a gay couple because you're uncomfortable because of the bible, and I don't want to because I think gay people are icky, is it ok for you not for me? Is discrimination ok if it's religious?
The only way requiring a baker to sell a cake is a violation of freedom of religion is if you argue that selling a cake to a gay couple implies acceptance or support of gay marriage. Then why wouldn't forcing me to sell a cake to a gay couple also be endorsing gay marriage, and therefore be a violation of my freedom of speech?
Can a baker refuse to sell a wedding cake for a second marriage or an interfaith marriage? There is strong biblical arguments against both of these things. So, a baker can refuse on these grounds as well I presume?
But, why do the bible verses matter? If I thought god opposed gay marriage but didn't have any bible verses to support that, would that then not be ok? If we require a biblical or otherwise scriptural argument, or require that a view is couched in a mainstream religion, then that is a clear violation of the establishment clause.
So then, lets say I believe that interracial relationships are sinful and opposed by god. Furthermore, I believe that black people are actually a race created by the devil to taint humanity, and to serve them at all is offensive to god. I deny service to any black person and refuse to sell any baked goods to an interracial couple based on these beliefs. Are you ok with that?
If not, suppose that I took a polygraph test that indicates that I sincerely believe these things. Is it ok now?